title: Team Sonic Racing

text: Team Sonic Racing is a 2019 kart racing game and a spin-off from Sega's "Sonic the Hedgehog" series. Controlling one of 15 characters from the series' cast, players compete in races using sports cars. Gameplay is from a third-person perspective, with players performing tricks, drifting, and collecting power-ups. "Team Sonic Racing" differs from traditional kart racers because of its focus on cooperative gameplay, similar to the kind featured in "Splatoon" (2015) and "Overwatch" (2016)—players are part of a team of racers and win races through efficiency rather than speed. Game modes include competing to earn points, time trials, customizing the racing rules, and a story-driven tutorial campaign.


title: Team Sonic Racing

text: Sumo Digital, which had previously worked on "Sonic & Sega All-Stars Racing" (2010) and "Sonic & All-Stars Racing Transformed" (2012), developed "Team Sonic Racing". Sonic Team head Takashi Iizuka conceived the cooperative gameplay, and Sumo Digital used the team-based "Sonic Heroes" (2003) as a point of reference. Unlike Sumo Digital's previous racing games, "Team Sonic Racing" only features "Sonic" characters, as the team wanted to expand the series' world and character roster. They aimed to make the game stand out compared to other racing games and developed it using a modified version of the "All-Stars" game engine. Musician Jun Senoue, who had not contributed to a major "Sonic" game since "Generations" (2011), composed the soundtrack.


title: Team Sonic Racing

text: "Team Sonic Racing" existence came to light when a Sumo Digital memo leaked in January 2018, with Sega confirming it the following May. Its marketing campaign included appearances at trade shows, a one-shot comic from IDW Publishing, and a two-part animated series. The game was released for the Nintendo Switch, PlayStation 4, Windows, and Xbox One in May 2019. A simplified version for iOS developed by Hardlight, Sonic Racing, was released via Apple Arcade in September 2019. The game was later released on Amazon Luna in March 2021. "Team Sonic Racing" received mixed reviews; its team-based gameplay, track designs, and music were praised, but the story mode and voice acting were criticized. Many critics also considered it inferior to the "Sega-All Stars" games.


title: Team Sonic Racing

text: "Team Sonic Racing" is a "Sonic the Hedgehog"-themed kart racing game featuring single-player and multiplayer modes. After selecting one of 15 characters from the series' cast, players participate in races using sports cars on courses thematically based on locations from the franchise. There are three types of racing classes: speed, technique, and power. Each type has its own unique abilities; for example, technique racers like Tails can drive over rough surfaces like grass without slowing down. The player views gameplay from a third-person perspective and runs over panels to get speed boosts, performs tricks in midair, and drifts to make sharp turns. Power-ups called Wisps can be collected from canisters with "?" marks and grant players temporary offensive and defensive advantages.


title: Team Sonic Racing

text: The gameplay differs from traditional racing games because of its focus on cooperative gameplay: the player is part of a team of racers and they must work together. While each player in a team still takes control of a single racer, they must also pay attention to how teammates are performing and share power-ups. Instead of winning races by simply finishing first, teams get points based on how they worked together. Thus, the most efficient team wins. Four teams of three compete, for a total of twelve racers at a time. Any character can be in a team; the player also has the option for each teammate to be the same character. Working together causes an "Ultimate" meter to be filled. When full, it can be activated to gain a temporary burst of speed. The meter's duration can be extended by hitting competing racers.


title: Team Sonic Racing

text: There are 21 tracks in total, including some returning from "Sonic & Sega All-Stars Racing" (2010) and "Sonic & All-Stars Racing Transformed" (2012), each split across seven zones and based on locations from main "Sonic" games. "Team Sonic Racing" features a variety of game modes, including Grand Prix, in which players compete to earn points; Time Trial, in which players race for the fastest time possible; and Exhibition, in which players can customize the racing rules. One mode, "Team Adventure", is a story-driven campaign that also includes a tutorial, as well as an original story explaining why the characters are racing. It is divided into chapters and players must complete missions like collecting as many rings as possible. Unlike the main game, the teams in Team Adventure are predetermined. Progressing through Team Adventure will unlock extras that can be used in the other modes.


title: Team Sonic Racing

text: Players can customize their vehicles, with new parts unlocked as they progress through the game. Customization options can be purchased using in-game currency called Mod Pods, which are earned by competing in races. Parts modify cars' handling, boost, acceleration, defense, and top speed, and players can also make aesthetic changes such as paint jobs and horn sounds. The game supports four-player local multiplayer, up to twelve online, and up to three in Team Adventure.


title: Team Sonic Racing

text: An alien tanuki named Dodon Pa sends invitations to Sonic the Hedgehog and several of his friends, inviting them to compete in a series of team-based races. He builds cars outfitted with advanced technology for each of the racers, offering them as a prize for the winning team. Though they are skeptical of Dodon Pa's motivations, Sonic and the others agree. The competition takes them across the world, with Dodon Pa pitting them against increasingly difficult challenges.


title: Team Sonic Racing

text: The racers remain suspicious of Dodon Pa, believing he may be working with Sonic's longtime nemesis Doctor Eggman. Investigating further, they discover he is king of the planet Donpa Kingdom and the president of the Donpa Motors automotive corporation. The company is constructing an Ultimate Energy Engine, which gains power from teamwork. Intending it for philanthropic use, Dodon Pa has been using the races to gather research data for the engine and generate energy to power it.


title: Team Sonic Racing

text: After unsuccessfully attempting to steal the engine, Eggman and his henchmen kidnap Dodon Pa and hold him hostage on their battleship. Eggman deceives Dodon Pa into finishing the engine for him, forcing Sonic and the others to continue racing to power it. Eggman installs the engine into a doomsday robot, but it goes haywire and destroys the battleship. Sonic and his friends manage to rescue Dodon Pa as the ship explodes, though the cars are destroyed in the process. A grateful Dodon Pa builds everyone new cars, and they prepare to race again.


title: Team Sonic Racing

text: The British video game developer Sumo Digital developed "Team Sonic Racing" for the Nintendo Switch, PlayStation 4, Windows, and Xbox One. It was Sumo Digital's third racing game featuring the "Sonic" intellectual property (IP), following "Sonic & Sega All-Stars Racing" and "Sonic & All-Stars Racing Transformed". Sega chose Sumo Digital to develop the game because of its experience with the "Sonic" IP. Development began before the completion of "Sonic Mania" and "Sonic Forces" in 2017. Unlike those games, which featured action-oriented gameplay, "Team Sonic Racing" was aimed at casual gamers. The majority of the staff did not work on the previous games, although some who did were contacted for advice. The lead designer of the game was Richard Acherki, while Sonic Team head Takashi Iizuka served as producer. "Team Sonic Racing" was Acherki's first game at Sumo Digital. According to Acherki, the proprietary game engine "Team Sonic Racing" runs on is a modified version of the one used to develop the "Sonic & Sega All-Stars Racing" games, and allowed them to easily port the game across platforms.


title: Team Sonic Racing

text: Unlike the "Sonic & Sega All-Stars" games, which featured various Sega franchises, "Team Sonic Racing" solely focuses on "Sonic". Sega's community manager Aaron Webber said that "Team Sonic Racing" is not a sequel to "Sonic & All-Stars Racing Transformed" and is "very, very different" from previous "Sonic" racers. Iizuka explained that the team wanted to make a game that took place solely in the "Sonic" universe, which is why it does not bear the "All-Stars" name. He noted Sega used to release a variety of racing games such as "Out Run" (1986) and "Daytona USA" (1992), and said "Team Sonic Racing" continues this tradition. Webber added that the team wanted to expand the world and character roster of "Sonic", and designer Derek Littlewood said setting the game in the "Sonic" universe allowed them use to the series' "full suite" of characters and elements. One of Sumo Digital's goals was to "provide plenty of fan service and also [give] people something new to look at and experience." Designer Ben Wilson called working on a "Sonic" game "surreal" and said the team enjoyed working with Sega. The game does not support cross-platform multiplayer, which Iizuka stated is because of technical constraints.


title: Team Sonic Racing

text: Sumo Digital wanted to make "Team Sonic Racing" stand out compared to other racing games, and with the engine of previous games they had a solid foundation to build a new experience. Iizuka suggested that they design it so it was easy for beginners. Sumo Digital also wanted to build on the gameplay of "Sonic & Sega All-Stars Racing Transformed", which many players enjoyed. Iizuka conceived the team-based gameplay after watching his son play a kart racing game with his friends. He observed that they were not all happy and pondered how they could all enjoy the game. Observing other games, Sumo Digital found that team gameplay was popular; noting that racing games were largely single-player experiences, they decided combining the concepts would create a unique and exciting experience. Iizuka said Sumo Digital was not inspired by other kart racing games like "Mario Kart 8" (2014) because the team wanted to make a game that emphasized teamwork instead of "a network game", citing "Splatoon" (2015) and "Overwatch" (2016) as examples of the cooperative gameplay "Team Sonic Racing" was designed to resemble. He also found it surprising there were few team-based racing games available.


title: Team Sonic Racing

text: Designing the game was challenging because the teamwork aspect was an unusual concept for a racing game. Iizuka and the team found that, if the cooperative gameplay was too prominent, it would hamper with the fluidity of the gameplay. Sumo Digital used "Sonic Heroes" (2003), which features team-based gameplay, as a point of reference. Other difficulties arose from choosing characters for the roster. For instance, Vector the Crocodile, traditionally seen as a member of the Chaotix in "Sonic" games, is paired with Blaze the Cat and Silver the Hedgehog in "Team Sonic Racing", which led to considerable debate among the team. They also had a hard time choosing courses with a variety of atmospheres. Each character received a unique car designed to reflect their individuality, while custom parts were made separately. "Team Sonic Racing" features several new versions of the Wisp power-ups from previous "Sonic" games. The "Sega All-Stars" games included general power-ups since they featured multiple franchises, but since "Team Sonic Racing" features simply "Sonic", Sumo Digital unified the power-ups with Wisps. The team worked with the Japanese Sonic Team staff to get approval for their concepts.


title: Team Sonic Racing

text: Jun Senoue composed the soundtrack in his first major work in the "Sonic" series since "Sonic Generations" (2011), while Richard Jacques, Tee Lopes, Tyler Smyth of DangerKids, Tomoya Ohtani, chip-tune artist TORIENA and the EDM group Hyper Potions also contributed. The game's theme song, "Green Light Ride", was performed by Senoue's band Crush 40. Iizuka said the team needed "cool" music that would "influence the player's excitement", which led him to ask Senoue to compose the score. He composed each track individually, collaborating with a different musician for each one.


title: Team Sonic Racing

text: Rumors of a new "Sonic" racing game arose in January 2018, when an internal Sumo Digital memo mentioning an "unannounced karting game" based on an "established global IP" leaked. Sumo Digital's history with "Sonic" caused speculation that it was developing a new "Sega All-Stars" title, which Webber denied. Despite his response, several toy companies alluded to a future "Sonic" kart racing game in February 2018. For example, a representative for the company Zappies reported at the Spielwarenmesse toy fair in Nuremberg that a third "Sonic" kart racing game was in development and that it planned to produce promotional toy figures. "Sonic" fans noted Webber's comments just alluded to the "Sega All-Stars" name and did not discount the premise of a new "Sonic" racing game, and further rumors of a game without any other Sega IPs involved arose later in February. Sega scheduled a "Sonic"-related announcement for its March 16, 2018 show at the SXSW convention. While Sega did not reveal the racing game there, the official series Twitter account teased it.


title: Team Sonic Racing

text: In May 2018, after the game leaked in a Walmart retail listing, Sega confirmed "Team Sonic Racing" was in development. "Eurogamer" expressed disappointment that it did not include any non-"Sonic" characters as playable racers, which its writer believed was one of the best things about "Sonic & Sega All Stars Racing" and its sequel. However, he remained optimistic, believing Sumo Digital's experience with "Sonic" would ensure the game would be a similar, "fundamentally brilliant arcade racer". Sega initially slated "Team Sonic Racing" for release in late 2018, but delayed it to May 21, 2019, that October to give Sumo Digital more development time. Iizuka later clarified that there were problems with the online mode that took more time than anticipated to fix. The game was released for Amazon Luna on March 11, 2021.


title: Team Sonic Racing

text: A demo version was playable at E3 2018 in June. The demo, which featured one track and six playable characters, was described by "Kotaku" as underwhelming, unfavorably comparing it to "Mario Kart". "Kotaku" argued the demo lacked ambition and called its character lineup shallow, especially when compared to that of "Sonic & All-Stars Racing Transformed". A more optimistic opinion came from "IGN": although he considered the power-ups generic, the writer felt the game still had a good foundation and that the team gameplay was satisfying. "Hardcore Gamer" nominated it as E3's best racing game, but it lost to "Forza Horizon 4". Sega released a trailer to promote the game at E3, featuring the theme song and an in-depth look at the gameplay. Another demo was playable at Gamescom in August 2018. More details were revealed, including the new character Dodon Pa, aspects of the story, and racetracks based on levels in "Sonic the Hedgehog 3" (1994) and "Sonic Unleashed" (2008). The game won the "Best Casual Game" award at the 2018 Gamescom Awards. "Team Sonic Racing" was also present at PAX West in August, where attendees were given an exclusive poster, and the Tokyo Game Show in November.


title: Team Sonic Racing

text: IDW Publishing released a promotional one-shot comic book, written by "Teenage Mutant Ninja Turtles" scribe Caleb Goellner and illustrated by "Sonic" comic artist Adam Bryce Thomas, in December 2018. The story is set before the game's events and features Sonic, Tails, Knuckles, and their friends traveling to a mysterious planet and preventing "an old foe" from obtaining new technology. At SXSW in March 2019, the first episode of a two-part tie-in animated series, "Team Sonic Racing Overdrive", was released, followed by the second episode in April. The series' animation was handled by Tyson Hesse and Neko Production, who previously produced the "Sonic Mania" (2017) tie-in "Sonic Mania Adventures". On launch day, Sega released a live-action trailer set in a supermarket, featuring a cameo from Iizuka. Sumo Digital chose to offer all content at launch instead of selling some as downloadable content, and not to include microtransactions.


title: Team Sonic Racing

text: "Sonic Racing", a simplified version developed by Hardlight, was released for iOS on September 19, 2019, as a launch title for Apple's Apple Arcade subscription service. The game was released as part of a deal between Apple and Sega, and Sega does not plan to release it on other platforms.


title: Team Sonic Racing

text: According to review aggregator Metacritic, "Team Sonic Racing" received "mixed or average reviews". "Screen Rant" observed that critics generally deemed it fun but inferior to the "Sega All-Stars" titles and "Mario Kart 8", which they felt were presented better.


title: Team Sonic Racing

text: Many critics of the game praised the team-based game play and the track designs as well. "IGN" stated, "Team Sonic Racing nails what matters most: speed and finesse on the racetrack. The new team system is a fantastic evolution of the arcade racing formula that gives you a real reason to work together, and there’s a litany of customization options to keep you coming back to these excellent tracks to earn more." Brian Shia of "Game Informer" stated, "Team Sonic Racing delivers a fun, easy-to-play experience that bolsters its adequate gameplay with distinct flavors to help it stand out from the rest of the genre." "Nintendo Life" gave the game a positive review, stating, "It’s strangely satisfying when you send some rockets to your 7th place chum and see their ranking climb a few moments later. Even though you’re just watching a number change, there’s an odd feeling of teamwork done well."


title: Team Sonic Racing

text: Many were critical of the game's story mode. Game Informer also stated, "The Team Adventure story mode is an inconsequential narrative told through still character images over background environments, making the uninteresting plot even less engaging." "GamesRadar+" was also critical of the game's story mode stating, "Team Sonic Racing's campaign includes seven chapters of races, as well as other types of modes like ring collection, target smashes, and elimination rounds, tied together by horribly boring cutscenes made up of static character art. If you're looking to handle the majority of this one alone then the campaign will be your only option. Outside time trials, local play, and online multiplayer, there isn't much else you can play through when you first start out."


title: Team Sonic Racing

text: The Nintendo Switch version of "Team Sonic Racing" sold 3,339 copies during its first week on sale in Japan, making it the thirteenth bestselling retail game of the week. The PlayStation 4 version sold 2,432 copies during the same week, placing it at number sixteen on the retail chart. It debuted at the top of the UK all-format sales charts—the first "Sonic" game to do so since "Mario & Sonic at the Olympic Games" in 2008—with the PlayStation 4 version selling the most copies. Its launch sales doubled that of "Sonic & All Stars Racing: Transformed". In 2021, the game was listed among one of Sega's best selling titles of that year.


title: Team Sonic Racing

text: The game was nominated for best racing game at the 2018 Game Critics Awards and 2019 Independent Game Developers' Association Awards.


title: C.S.D. Independiente del Valle

text: Club de Alto Rendimiento Especializado Independiente del Valle, known simply as Independiente del Valle, is a professional football club based in Sangolquí, Ecuador, that currently plays in the Ecuadorian Serie A.


title: C.S.D. Independiente del Valle

text: Founded in 1958, the club plays its home games at , which opened in March 2021 and has a capacity for 12,000. In the 2013 Ecuadorian Serie A Independiente finished runner-ups, and they won their first league title in 2021.


title: C.S.D. Independiente del Valle

text: In CONMEBOL competitions, it reached the final of the 2016 Copa Libertadores after famously defeating powerhouses River Plate and Boca Juniors, it won its first ever title in 2019, Three years later the club would become one of the few two-time Sudamericana champions after defeating São Paulo in the 2022 final.


title: C.S.D. Independiente del Valle

text: The club is also known for producing youth talent, and a good example of this is the club's U-20 Copa Libertadores title in 2020. Some well-known footballers the club has produced are Jefferson Montero, Junior Sornoza, Arturo Mina, Cristian Ramírez, Moisés Caicedo and Piero Hincapié.


title: C.S.D. Independiente del Valle

text: The club was founded on 1 March 1958 as Club Deportivo Independiente by Jose Terán, a football fan from Sangolquí, along with a group of friends including José Díaz, Jorge Atapuma, the "Negro" Sanguano, Tomás Zaldumbide and "Marino" Guayasamín. In 1977, two years after the death of José Terán, the club's name was changed to Club Social y Deportivo Independiente José Terán in honor of its founder. The name and initial club colors (red and white) were inspired by Argentine club Club Atlético Independiente.


title: C.S.D. Independiente del Valle

text: In 1995 the club reached the Segunda Categoría (3rd Division) for the second time. After winning the Segunda Categoría in 2007, the club changed its name to "Independiente del Valle" and adopted the current colors (blue and black). "Los Negriazules" achieved promotion to the Ecuadorian Serie A for the first time ever in the 2010 season, after winning the .


title: C.S.D. Independiente del Valle

text: In the 2013 Serie A, the club finished runner-up on the aggregate table. Independiente del Valle made its first international participation that same year, in the 2013 Copa Sudamericana, where it was eliminated in the second stage by Universidad de Chile after having beat Venezuelan club Deportivo Anzoategui in the first stage. The next year, the Ecuadorian club made its first Copa Libertadores participation and second overall international participation, with the 2014 edition. In that edition, the club was eliminated after placing 3rd in their group.


title: C.S.D. Independiente del Valle

text: In July 2014, the club officially changed its name from "Independiente del Valle" to Club de Alto Rendimiento Especializado Independiente del Valle. Although the club had changed its name already, it had never been made official by the Ecuadorian Football Federation until that point.


title: C.S.D. Independiente del Valle

text: Independiente del Valle unexpectedly reached the finals of the 2016 Copa Libertadores with incredible odds, being compared to Leicester City's Premier League title that same year. Independiente began its knockout stage run by beating Copa Libertadores defending champions, Argentina's River Plate, in the round of 16 2–1 on aggregate. In the quarter-finals they defeated Pumas UNAM on penalties 5–3, after an aggregate score of 3–3. The club subsequently faced Argentina's giant Boca Juniors in the semi-final, defeating them 5–3 on aggregate, including a 3–2 victory at the famous La Bombonera stadium. In the finals, the Ecuadorians faced Colombia's Atlético Nacional. In the first leg played at Estadio Olímpico Atahualpa on 20 July, the match finished 1–1. Independiente's fairy tale story came to a conclusion after a 1–0 loss in the second leg with the series ending 2–1 in favor of the Colombians.


title: C.S.D. Independiente del Valle

text: In November 2019, Independiente del Valle played their first ever Copa Sudamericana final, and only its second ever CONMEBOL final, where they defeated Club Atlético Colón 3–1 in Asunción. This was the Ecuadorian club's first ever historic title. It was considered a major upset because Colón had a richer history and a much bigger fanbase, with around 40,000 fans at the stadium versus only 500 Ecuadorians.


title: C.S.D. Independiente del Valle

text: In February 2020, the club lost the 2020 Recopa Sudamericana against the champion of the 2019 Copa Libertadores, Flamengo. The first leg in Quito was a 2–2 draw, but in the second leg at Estadio Maracana, Flamengo won 3–0 and became the champion with a 5–2 aggregate score.


title: C.S.D. Independiente del Valle

text: For international tournaments the club use larger stadiums like the Estadio Olímpico Atahualpa in Quito that has a 38,500-capacity.


title: C.S.D. Independiente del Valle

text: In March 2021, the club opened a new 12,000-capacity stadium called . It meets modern FIFA standards and is able to hold international matches, unlike their old stadium. It also has three grandstands with a roof, compared to Estadio Rumiñahui, which only had one grandstand.


title: C.S.D. Independiente del Valle

text: The club has its own training center located in Sangolquí which is called "Centro de Alto Rendimiento". It has seven football fields, one of them with artificial grass. The training center also has rooms to accommodate players, dining room, parking, a gym (for the first-team and reserves), indoor pool and administrative offices.


title: C.S.D. Independiente del Valle

text: Since 2018, the club has a reserve team in the Ecuadorian Serie B, formerly named "Alianza Cotopaxi SC". After the promotion, the club changed name to C.D. Independiente Juniors.


title: C.S.D. Independiente del Valle

text: The following players were chosen to represent their country at the FIFA World Cup while contracted to Independiente del Valle.


title: Economic policy

text: The economy of governments covers the systems for setting levels of taxation, government budgets, the money supply and interest rates as well as the labour market, national ownership, and many other areas of government interventions into the economy.


title: Economic policy

text: Most factors of economic policy can be divided into either fiscal policy, which deals with government actions regarding taxation and spending, or monetary policy, which deals with central banking actions regarding the money supply and interest rates.


title: Economic policy

text: Such policies are often influenced by international institutions like the International Monetary Fund or World Bank as well as political beliefs and the consequent policies of parties.


title: Economic policy

text: Almost every aspect of government has an important economic component. A few examples of the kinds of economic policies that exist include:


title: Economic policy

text: Stabilization policy attempts to stimulate an economy out of recession or constrain the money supply to prevent excessive inflation.


title: Economic policy

text: Policy is generally directed to achieve particular objectives, like targets for inflation, unemployment, or economic growth. Sometimes other objectives, like military spending or nationalization are important.


title: Economic policy

text: To achieve these goals, governments use policy tools which are under the control of the government. These generally include the interest rate and money supply, tax and government spending, tariffs, exchange rates, labor market regulations, and many other aspects of government.


title: Economic policy

text: Government and central banks are limited in the number of goals they can achieve in the short term. For instance, there may be pressure on the government to reduce inflation, reduce unemployment, and reduce interest rates while maintaining currency stability. If all of these are selected as goals for the short term, then policy is likely to be incoherent, because a normal consequence of reducing inflation and maintaining currency stability is increasing unemployment and increasing interest rates.


title: Economic policy

text: This dilemma can in part be resolved by using microeconomic supply-side policy to help adjust markets. For instance, unemployment could potentially be reduced by altering laws relating to trade unions or unemployment insurance, as well as by macroeconomic (demand-side) factors like interest rates.


title: Economic policy

text: For much of the 20th century, governments adopted discretionary policies like demand management designed to correct the business cycle. These typically used fiscal and monetary policy to adjust inflation, output and unemployment.


title: Economic policy

text: A discretionary policy is supported because it allows policymakers to respond quickly to events. However, discretionary policy can be subject to dynamic inconsistency: a government may say it intends to raise interest rates indefinitely to bring inflation under control, but then relax its stance later. This makes policy non-credible and ultimately ineffective.


title: Economic policy

text: A rule-based policy can be more credible, because it is more transparent and easier to anticipate. Examples of rule-based policies are fixed exchange rates, interest rate rules, the stability and growth pact and the Golden Rule. Some policy rules can be imposed by external bodies, for instance, the Exchange Rate Mechanism for currency.


title: Economic policy

text: A compromise between strict discretionary and strict rule-based policy is to grant discretionary power to an independent body. For instance, the Federal Reserve Bank, European Central Bank, Bank of England and Reserve Bank of Australia all set interest rates without government interference, but do not adopt rules.


title: Economic policy

text: Another type of non-discretionary policy is a set of policies that are imposed by an international body. This can occur (for example) as a result of intervention by the International Monetary Fund.


title: Economic policy

text: The first economic problem was how to gain the resources it needed to be able to perform the functions of an early government: the military, roads and other projects like building the Pyramids.


title: Economic policy

text: Early governments generally relied on tax in kind and forced labor for their economic resources. However, with the development of money came the first policy choice. A government could raise money through taxing its citizens. However, it could now also debase the coinage and so increase the money supply.


title: Economic policy

text: Early civilizations also made decisions about whether to permit and how to tax trade. Some early civilizations, such as Ptolemaic Egypt adopted a closed currency policy whereby foreign merchants had to exchange their coin for local money. This effectively levied a very high tariff on foreign trade.


title: Economic policy

text: By the early modern age, more policy choices had been developed. There was considerable debate about mercantilism and other restrictive trade practices like the Navigation Acts, as trade policy became associated with both national wealth and with foreign and colonial policy.


title: Economic policy

text: Throughout the 19th Century, monetary standards became an important issue. Gold and silver were in supply in different proportions. Which metal was adopted influenced the wealth of different groups in society.


title: Economic policy

text: With the accumulation of private capital in the Renaissance, states developed methods of financing deficits without debasing their coin. The development of capital markets meant that a government could borrow money to finance war or expansion while causing less economic hardship.


title: Economic policy

text: The same markets made it easy for private entities to raise bonds or sell stock to fund private initiatives.


title: Economic policy

text: The business cycle became a predominant issue in the 19th century, as it became clear that industrial output, employment, and profit behaved in a cyclical manner. One of the first proposed policy solutions to the problem came with the work of Keynes, who proposed that fiscal policy could be used actively to ward off depressions, recessions and slumps. The Austrian School of economics argues that central banks create the business cycle. After the dominance of monetarismry and neoclassical thought that advised limiting the role of government in the economy in the second half of the twentieth century, the interventionist view has once more dominated the economic policy debate in response to the 2007-2008 financial crisis,


title: Economic policy

text: A recent trend originating from medicine is to justify economic policy decisions with best available evidence. While the previous approaches have been focused on macroeconomic policymaking aimed at sustaining promoting economic development and counteracting recessions, EBP is oriented towards all types of decisions concerned not only with anti-cyclical development but primarily with the growth-promoting policies. To gather evidence for such decisions, economists conduct randomized field experiments. The work of Banerjee, Duflo, and Kremer, the 2019 Nobel Prize laureates exemplifies the gold type of evidence. However, the emphasis put on experimental evidence by the movement of evidence-based policy (and evidence-based medicine) results from the narrowly construed notion of intervention, which encompasses only policy decisions concerned with policymaking aimed at modifying causes to influence effects. In contrast to this idealized view of evidence-based policy movement, economic policymaking is a broader term that includes also institutional reforms and actions that do not require causal claims to be neutral under interventions. Such policy decisions can be grounded in, respectively, mechanistic evidence and correlational (econometric) studies.


title: Bile bear

text: Bile bears, sometimes called battery bears, are bears kept in captivity to harvest their bile, a digestive fluid produced by the liver and stored in the gallbladder, which is used by some traditional Asian medicine practitioners. It is estimated that 12,000 bears are farmed for bile in China, South Korea, Laos, Vietnam, and Myanmar. Demand for the bile has been found in those nations as well as in some others, such as Malaysia and Japan.


title: Bile bear

text: The bear species most commonly farmed for bile is the Asiatic black bear ("Ursus thibetanus"), although the sun bear ("Helarctos malayanus"), brown bear ("Ursus arctos") and every other species are also used (the only exception being the giant panda which does not produce UDCA). Both the Asiatic black bear and the sun bear are listed as Vulnerable on the Red List of Threatened Animals published by the International Union for Conservation of Nature. They were previously hunted for bile but factory farming has become common since hunting was banned in the 1980s.


title: Bile bear

text: The bile can be harvested using several techniques, all of which require some degree of surgery, and may leave a permanent fistula or inserted catheter. A significant proportion of the bears die because of the stress of unskilled surgery or the infections which may occur.


title: Bile bear

text: Farmed bile bears are housed continuously in small cages which often prevent them from standing or sitting upright, or from turning around. These highly restrictive cage systems and the low level of skilled husbandry can lead to a wide range of welfare concerns including physical injuries, pain, severe mental stress and muscle atrophy. Some bears are caught as cubs and may be kept in these conditions for up to 30 years.


title: Bile bear

text: The value of the bear products trade is estimated as high as $2 billion. The practice of factory farming bears for bile has been extensively condemned, including by Chinese physicians.


title: Bile bear

text: Bear bile and gallbladders, which store bile, are ingredients in traditional Chinese medicine (TCM). Its first recorded use is found in "" ("Newly Revised Materia Medica", Tang Dynasty, 659 CE). The pharmacologically active ingredient contained in bear bile and gallbladders is ursodeoxycholic acid (UDCA); bears are the only mammals to produce significant amounts of UDCA.


title: Bile bear

text: Initially, bile was collected from wild bears which were killed and the gall and its contents cut from the body. In the early 1980s, methods of extracting bile from live bears were developed in North Korea and farming of bile bears began. This rapidly spread to China and other regions. Bile bear farms were started to reduce hunting of wild bears, with the hope that if bear farms raised a self-sustaining population of productive animals, poachers would have little motivation to capture or kill bears in the wild.


title: Bile bear

text: The demand for bile and gallbladders exists in Asian communities throughout the world, including the European Union and the United States. This demand has led to bears being hunted in the US specifically for this purpose.


title: Bile bear

text: It has been estimated that 50–60 per cent of bears die from complications caused by the surgery or improper post-surgical care.


title: Bile bear

text: Cubs are sometimes caught in the wild and used to supplement numbers held captive in farms. In 2008, it was reported that bear farms were paying the equivalent of US$280 to US$400 for a wild bear cub.


title: Bile bear

text: Bile extraction begins at three years-of-age and continues for a minimum of five to ten years. Some bears may be kept in cages for bile extraction for 20 years or more. A bear can produce 2.2 kg of bile over a 5-year production life.


title: Bile bear

text: When the bears outlive their productive bile-producing years (around 10 years old), they are often slaughtered and harvested for their other body parts such as meat, fur, paws and gallbladders; bear paws are considered a delicacy.


title: Bile bear

text: To facilitate the bile extraction process, mature bears are usually kept in small cages measuring approximately 130 x 70 x 60 cm. These cages are so small they prevent the bears from being able to sit upright, stand or turn around. Some bears are kept in crush cages, the sides of which can be moved inwards to restrain the bear. The HSUS reports that some bears are moved to a crush cage for milking, but the remainder of the time live in a cage large enough to stand and turn around.


title: Bile bear

text: Bile bears are often subjected to other procedures which have their own concomitant ethical and welfare concerns. These include declawing in which the third phalanx of each front digit is amputated to prevent the bears from self-mutilating or harming the farm workers. They may also have their hind teeth removed for the same reasons. These procedures are often conducted by unskilled farm staff and may result in the bears experiencing constant pain thereafter.


title: Bile bear

text: Pathology reports have shown that bile from sick bears is often contaminated with blood, pus, faeces, urine, bacteria and cancer cells.


title: Bile bear

text: International concern about the welfare of bile bears began in 1993. Many bile bear farms have little or no veterinary supervision and the animal husbandry is often conducted by non-skilled attendants. In combination with the impacts of small cage sizes, their spacing and lack of internal structures, there are several indicators of poor welfare.


title: Bile bear

text: Elevated corticosteroid concentrations are a widely acknowledged indicator of physiological stress. Corticosteroid concentrations in the hair of Asiatic black bears relocated from a bile farm to a bear rescue centre fell between 12 and 88% over 163 days.


title: Bile bear

text: Other physiological indicators of stress and potentially reduced welfare include growth retardation and ulcers.


title: Bile bear

text: A 2000 survey revealed that bile bears suffered from sores, skin conditions, ectoparasites, hair loss, bone deformities, injuries, swollen limbs, dental and breathing problems, diarrhoea and scarring.


title: Bile bear

text: One survey of 165 bears removed from a farm showed that (out of 181 free-drip bears), 163 (90%) had cholecystitis, 109 (66%) had gallbladder polyps, 56 (34%) had abdominal herniation, 46 (28%) had internal abscessation, 36 (22%) had gallstones, and 7 (4%) had peritonitis. Many of the bears had a combination of these conditions.


title: Bile bear

text: Academic sources have reported that bile bears exhibit abnormal behaviours such as stereotypies, lethargy, anxiety, and self-mutilation.


title: Bile bear

text: The Chinese media reported a story in which a mother bear, having escaped her cage, strangled her own cub and then killed herself by intentionally running into a wall. Animals Asia attempted to verify the story after it went viral, and concluded it likely did not happen.


title: Bile bear

text: Farmed bile bears live to an average age of five years old whereas healthy captive bears can live up to 35 years of age and wild bears for between 25 and 30 years.


title: Bile bear

text: In 1994, Chinese authorities announced that no new bear farms would be licensed and in 1996, issued a special notice stating that no foreign object was allowed to be inserted into a bear body. No bears younger than 3 years of age and lighter than 100 kg were to be used for bile extraction, and bears could be confined in cages only during the time of bile extraction. The authorities required the adoption of the free-drip method which necessitates the creation of an artificial fistula between the gallbladder and the abdominal wall by opening a cut into the gallbladder.


title: Bile bear

text: In 2006, the Chinese State Council Information Office said that it was enforcing a "Technical Code of Practice for Raising Black Bears", which "requires hygienic, painless practice for gall extraction and make strict regulations on the techniques and conditions for nursing, exercise and propagation." However, a 2007 veterinary report published by the Animals Asia Foundation (AAF) stated that the Technical Code was not being enforced and that many bears were still spending their entire lives in small extraction cages without free access to food or water. The report also noted that the free-dripping technique promoted in the Technical Code was unsanitary as the fistula was an open portal through which bacteria could infiltrate the abdomen. The report also stated that surgeries to create free-dripping fistulae caused bears great suffering as they were performed without appropriate antibiotics or pain management and the bears were repeatedly exposed to this process as the fistulae often healed over. The free-dripping method still requires the bears to be prodded with a metal rod when the wound heals over and under veterinary examination, some bears with free-dripping fistulae were actually found to have clear perspex catheters permanently implanted into their gallbladders. In addition to the suffering caused by infection and pain at the incision site, 28% of fistulated bears also experience abdominal hernias and more than one-third eventually succumb to liver cancer, believed to be associated with the bile-extraction process.


title: Bile bear

text: In South Korea, bear farming was declared illegal in 1992. However, it was reported in 2008 that over 1,300 bears were still on 108 farms where farmers were hoping that legal farming would resume. , wild bears over the age of ten could still be legally killed for their gallbladders in South Korea.


title: Bile bear

text: The Vietnamese government in 2005 made it illegal to extract bear bile and made a commitment to phase out bear farming. In 2008, there were still 3,410 bears on farms in Vietnam.


title: Bile bear

text: Officially, 7,600 captive bears are farmed in China. According to Chinese officials, 10,000 wild bears would need to be killed each year to produce as much bile. Government officials see farming as a reasonable answer to the loss of wild bears from poaching and are insouciant about animal welfare concerns. However, the government's agreement to allow the rescue of 500 bears may represent a softening of this stance.


title: Bile bear

text: Earthtrust reported in 1994 that demand for bear parts from South Korea and Taiwan was one of the greatest threats to bear populations worldwide. Due to partnerships between some South Korean travel companies and South Korean bear farmers, 'bear bile tourism' from the country has reportedly helped fuel the farming industry in China and Vietnam.


title: Bile bear

text: World Animal Protection reported in 2002 that Japan's demand for bear bile remained at a level of at least 200 kg per year which in theory would require 10,000 bears killed to be satisfied. Legislation and enforcement for bear products in the country has also been lacking.


title: Bile bear

text: A 2015 report indicated that the illegal trade in bear bile and gallbladder for traditional medicine is open and widespread across Malaysia and is potentially a serious threat to wild bears. In a survey of 365 traditional medicine shops across Malaysia, 175 (48%) claimed to be selling bear gallbladders and medicinal products containing bear bile.


title: Bile bear

text: Some supporters of bile bear farms argue, "Wildlife farming offers, at first glance, an intuitively satisfying solution: a legal trade can in principle be created by farming animals to assuage demand for wild animals which thus need not be harvested."


title: Bile bear

text: Nonetheless, bears continue to be hunted in the wild to supply the bile farms. A survey in 2000 reported that almost all of the farms in the study supplemented their captive population of bile bears with wild-caught bears. This is claimed to be necessary because of difficulties with captive breeding. Consumers of bear bile have a strong preference for bile produced from wild bears; bile from farms may, therefore, not be a perfect substitute for bile from wild bears. Bear farming in Laos may be increasing the incentive to poach wild bears.


title: Bile bear

text: A review of multiple types of wildlife tourist attractions concluded that bile bear farms had negative impacts on both animal welfare and conservation.


title: Bile bear

text: In the late 1980s, U.S. park rangers began finding bear carcasses missing only gallbladders and paws. Initially, it was considered that occasional hunters were the cause, but investigations uncovered evidence that large commercial organizations were dealing in poaching and smuggling. During a three-year operation (Operation SOUP) ending in 1999, 52 people were arrested and 300 gallbladders seized in Virginia. Another investigation in Oregon led police to bring racketeering charges against an organisation that poached an estimated 50 to 100 bears per year for a decade. It was estimated in 2008 that in North America, 40,000 American black bears are illegally poached for their gallbladders and paws each year.


title: Bile bear

text: The pharmacologically active ingredient contained in bear bile is ursodeoxycholic acid (UDCA). This can be synthesized using cow or pig bile, or even using no animal ingredients. The generic drug name is Ursodiol and it is now being widely produced under brand names such as Actigall, Urso, Ursofalk, Ursogal and Ursotan. It was estimated in 2008 that 100,000 kg of synthetic UDCA was already being used each year in China, Japan and South Korea, and that the total world consumption may be double this figure. However, many traditional doctors still consider natural (but farmed) UDCA a superior product.


title: Bile bear

text: In Japan, UDCA has been synthesised from cow galls, as a by-product of the meat industry, since 1955. It is also produced in the U.S. by Ciba-Geigy.


title: Bile bear

text: In 2014, Kaibao Pharmaceuticals, which supplies approximately half of the bear bile consumed in China, stated it is developing another synthetic source derived from poultry bile.


title: Bile bear

text: The world population of Asiatic black bears decreased between 30% to 49% between 1980 and 2010. Although their reliability is unclear, range-wide estimates of 5–6,000 bears have been presented by Russian biologists. Rough density estimates without corroborating methods or data have been made in India and Pakistan, resulting in estimates of 7–9,000 in India and 1,000 in Pakistan. Unsubstantiated estimates from China give varying estimates between 15,000 and 46,000, with a government estimate of 28,000. Some estimates put the current (2015) total Asian worldwide population as low as 25,000.


title: Bile bear

text: The World Society for the Protection of Animals has been reported in 2011 as saying that more than 12,000 bears are currently estimated to be housed in both illegal and legal bear farms across Asia.


title: Bile bear

text: World Animal Protection conducted a study in 1999 and 2000, and estimated that 247 bear bile farms in China were holding 7,002 bears, though the Chinese government called the figures "pure speculation." The Chinese consider bear farms a way to reduce the demand on the wild bear population. Officially, 7,600 captive bears are farmed in China. According to Chinese officials, 10,000 wild bears would need to be killed each year to produce as much bile. The government sees farming as a reasonable answer to the loss of wild bears from poaching. However, the government's agreement to allow the rescue of 500 bears may represent a softening of this stance.


title: Bile bear

text: China has been found to be the main source of bear bile products on sale throughout South-East Asia; this international trade in their parts and derivatives is strictly prohibited by the Convention on International Trade in Endangered Species of Wild Fauna and Flora.


title: Bile bear

text: In 2010, there were approximately 97 establishments in China keeping bile bears. This was a decrease from the mid-1990s, where Xinhua reported of 480 bear farms in the country.


title: Bile bear

text: In 2013, estimates of bears kept in cages in China for bile production range from 9,000 to 20,000 bears on nearly 100 domestic bear farms. One company (Fujian Guizhen Tang Pharmaceutical Co. Ltd) alone has more than 400 black bears to supply bile using the free drip method. The bile is harvested twice a day to collect a total of approximately 130 ml from each bear per day.


title: Bile bear

text: Before the existence of bear farms (i.e. pre-1980) the demand for bear bile in China was about 500 kilos annually. In 2008, the demand had risen to about 4,000 kilos annually.


title: Bile bear

text: In 2009, according to the South Korean Environment Ministry, 1,374 bears were raised at 74 farms across South Korea. In South Korea, it is legal to keep bears for bile and bears older than 10 years old can be harvested for their paws and organs. In 2012, the number of bears in South Korean farms have risen to about 1,600.


title: Bile bear

text: In Laos, the first farm was established in 2000. The number of farmed bears tripled from 2008 to 2012. In 2012, there were 121 Asiatic black bears and one sun bear on 11 commercial facilities. It is possible that all the bears were wild-caught domestically, or illegally imported internationally. This is in violation of both National and International law.


title: Bile bear

text: In Laos in 2011, bear bile was selling for 120,000 kip (US$15) per ml, half the average monthly wage of 240,000 kip. A 2019 survey of locals in Luang Prabang found that although attitudes towards bears and conservation were generally positive, awareness of cruelty in the bear farms was lacking, with 43.7% of respondents regarding bile consumption sourced from bear farms as acceptable.


title: Bile bear

text: A 2019 survey published by the Claremont Colleges of 206 older Northern Vietnamese locals found that roughly 44% of respondents knew at least one other person who had used bear products from farms in the past year, compared to 55.33% of those who did not. 8.72% of respondents listed protecting bears as one of the reasons a person would not use such products, compared to roughly 21% who listed quality or preferring different medicine as reasons.


title: Bile bear

text: The monetary value of the bile comes from the traditional prescription of bear bile by doctors practicing traditional medicine. Bear bile contains ursodeoxycholic acid. It is purchased and consumed to treat hemorrhoids, sore throats, sores, bruising, muscle ailments, sprains, epilepsy, reduce fever, improve eyesight, break down gallstones, act as an anti-inflammatory, reduce the effects of overconsumption of alcohol, and to 'clear' the liver. It is currently found in various forms for sale including whole gallbladders, raw bile, pills, powder, flakes, and ointment.


title: Bile bear

text: Because only minute amounts of bile are used in TCM, a total of 500 kg of bear bile is used by practitioners every year, but according to WSPA, more than 7,000 kg are being produced. The surplus has reportedly been used as ingredients in beauty products and non-traditional health tonics.


title: Bile bear

text: China's National Health Commission drew criticism in 2020 after reportedly recommending 'Tan Re Qing', a traditional medicine which contains the bile, to treat severe cases of COVID-19. Some South Korean bear bile farmers in the same year advertised that their products could also help with the coronavirus, drawing criticism from local animal rights groups.


title: Bile bear

text: Scientific studies have found bear bile to have anti-inflammatory, anti-microbial, and hepatoprotective effects.


title: Bile bear

text: The active ingredient in bear bile is ursodeoxycholic acid. Ursodeoxycholic acid has been shown to exert anti-inflammatory and protective effects in human epithelial cells of the gastrointestinal tract. It has been linked to regulation of immunoregulatory responses by regulation of cytokines, antimicrobial peptides defensins, and take an active part in increased restitution of wound in the colon. Moreover, UDCA's effects has been shown to have exert actions outside the epithelial cells.


title: Bile bear

text: Bear bile has also been shown in studies to be able to get rid of gallstones by dissolving them in the gallbladder.


title: Bile bear

text: Due to controversy around the use of bear farming to obtain bile, synthetic sources for ursodeoxycholic acid are currently being worked on and investigated. Scientists in China have been working on synthetic forms of bile products, so that scientists need not use animal sources for bile. In this way, it is hoped that in the future, bile can be created in methods that do not involve animal cruelty.


title: Bile bear

text: In 2011, the overall worldwide trade in bear parts, including bile, was estimated to be a $2 billion industry.


title: Bile bear

text: In 1970, 1 kg of bear gallbladder cost approximately US$200, but by 1990 the price had risen to between US$3,000 and US$5,000 per kg. In 2009, the market price for legally sold gallbladders in Hong Kong had risen to between US$30,000 and US$50,000 per kg. It was reported in 1991 that bear gallbladders and the like could sell in Seoul "for 10 times their price in China", with prices for one ranging from US$700 to US$3,292. In 2002, the pricier bear galls in Japan were reported to be selling for as much as US$83 per gram, and were either sourced domestically, or from Tibet or China.


title: Bile bear

text: A report published in 2013 stated that a poacher in North America can usually get US$100 to $150 for a gallbladder, but the organs can fetch $5,000 to $10,000 in the end-market once they are processed into a powder. The report also stated that the HSUS indicated a bear gallbladder can cost more than $3,000 in Asia. A TRAFFIC report estimated that prices for whole gallbladders were as low as $51.11 (Myanmar) and as high as $2,000 (Hong Kong SAR). For gallbladder by the gram, the least expensive was $0.11 per gram (Thailand) and the highest was $109.70 per gram (Japan).


title: Bile bear

text: There is huge profitability in the trade of bile powder. In 2007, while the wholesale price of bile powder was approximately US$410 per kg in China, the retail price increased from 25 to 50 fold in South Korea, and to 80 fold in Japan, i.e. US$33,000 per kg.


title: Bile bear

text: Pill prices ranged from as low as $0.38 per pill (Malaysia) to $3.83 per pill (Thailand). and in the U.S., approximately $1 per pill, which is an average price between the two countries.


title: Bile bear

text: In 2010, the Guizhentang Pharmaceutical company was one of the most successful bile extraction companies in China, paying some 10 million yuan in taxes. In 2012, the company tried to go public in the Shenzhen stock exchange and proposed to triple the company's stock of captive bears, from 400 to 1,200. This provoked a large backlash from activists, internet users and protesters. It was followed by a number of controversies along with public interviews. The company responded with demonstrations of the extraction process where the bears seemed unconcerned by the procedure, in an attempt to counter the allegations its business was cruel.


title: Band of Brothers (book)

text: Band of Brothers, subtitled, "E Company, 506th Regiment, 101st Airborne: From Normandy to Hitler's Eagle's Nest", by Stephen E. Ambrose is an examination of a parachute infantry company in the 101st Airborne Division in the European Theater during World War II. While the book treats the flow of battle, it concentrates on the lives of the soldiers in and associated with the company. The book was later adapted into a 2001 miniseries for HBO by Tom Hanks, Erik Jendreson, and Steven Spielberg, also titled "Band of Brothers."


title: Band of Brothers (book)

text: The book rests upon interviews Ambrose conducted with former members of E Company, 2nd Battalion, 506th Parachute Infantry Regiment of the 101st Airborne Division. The veterans were having a reunion at a hotel in New Orleans, Louisiana; the interviews were conducted as part of a project to collect oral histories of D-Day for the National D-Day Museum in New Orleans. Ambrose was intrigued with the bonds that had developed among the members of Easy Company. He circulated his drafts among the surviving members of the company, asked for input, and incorporated their ideas into later drafts. Ambrose wrote of the finished product, "We have come as close to the true story of Easy Company as possible."


title: Band of Brothers (book)

text: The book consists of a foreword, epigraph, and a maps section, followed by 19 chapters. There is an afterword and a brief author's bio after the chapters.


title: Band of Brothers (book)

text: "To all those members of the Parachute InfantryUnited States Army, 1941-1945who wear the Purple Heart not as a decorationbut as a badge of office."


title: Band of Brothers (book)

text: The epigraph is a quotation from Shakespeare's "Henry V", from which the title of the book is derived:


title: Arlington House, The Robert E. Lee Memorial

text: Arlington House is the historic family residence of Robert E. Lee, commander of the Confederate Army, and a national memorial in his honor serving as a museum, located in Arlington, Virginia. It is situated in the middle of Arlington National Cemetery, overlooking the Potomac River and the National Mall.


text: Built by Lee's father in law G.W.P. Custis in 1803-1818, Arlington House is a Greek Revival style mansion designed by the English architect George Hadfield. Its garden and adjoined structures are also preserved.


text: During the U.S. Civil War, the mansion was used as U.S. army headquarters and its grounds were selected as the site of Arlington National Cemetery, in part to ensure that Lee would never again be able to reside there. Arlington House is part of the Arlington National Cemetery Historical Region on the National Registry of Historic Places. Although the United States Department of the Army maintains Arlington National Cemetery, the National Park Service administers Arlington House. There, the U.S. flag flies at half-staff during funerals.


text: The mansion was built on the orders of George Washington Parke Custis, the foster son of George Washington and grandson of Martha Dandridge Custis Washington. Custis became a prominent resident of an area that was then known as Alexandria County, at the time a part of the District of Columbia.


text: Arlington House was built at a high point on a 1,100-acre (445 ha) estate that Custis's father, John Parke Custis, had purchased in 1778 and named "Mount Washington" ("Jacky" Custis died in 1781 at Yorktown after the British surrender). The younger Custis decided to build his home on the property in 1802 following the death of Martha Washington and three years after the death of George Washington. After acquiring the property, Custis renamed it "Arlington" after the Custis family's homestead on the Eastern Shore of Virginia.


text: Almost immediately, Custis began constructing Arlington House on his land. Hiring George Hadfield as architect, he constructed a mansion exhibiting the first example of Greek Revival architecture in America. Custis intended the mansion to serve as a living memorial to George Washington and a place for his collection of George Washington artifacts. Its design included elements similar to those of George Washington's house, Mount Vernon.


text: Construction began in 1803, eleven years after L'Enfant's Plan for the future "Federal City" (later called "Washington City", then Washington D.C.) had designated an area directly across the Potomac River to be the site of the "President's House" (later called the "Executive Mansion", now the White House) and the "Congress House" (now the United States Capitol). Custis located the building on a prominent hill overlooking the Georgetown-Alexandria Turnpike (at the approximate location of the present Eisenhower Drive in Arlington National Cemetery), the Potomac River and the growing Washington City on the opposite side of the river. The mansion was built using materials on site, though the building was interrupted by the War of 1812 (and material shortages after the British burned the American capital city). The Custis mansion's exterior was completed in 1818.


text: The north and south wings were completed in 1804. The large center section and the portico, presenting an imposing front 140 ft (43 m) long, were finished 13 years later. The house has two kitchens, a summer and a winter. The most prominent features of the house are the 8 massive columns of the portico, each 5 feet (1.5 m) in diameter.


text: Guests at the house included such notable people as Gilbert du Motier, Marquis de Lafayette, who visited in 1824 (see: Visit of the Marquis de Lafayette to the United States). At Arlington, Custis experimented with new methods of animal husbandry and other agriculture. The property also included Arlington Spring, a picnic ground on the banks of the Potomac that Custis originally built for private use but later opened to the public, eventually operating it as a commercial enterprise.


text: Custis married Mary Lee Fitzhugh. Their only child to survive to adulthood was Mary Anna Randolph Custis. Robert E. Lee, whose mother was a cousin of Mrs. Custis, frequently visited Arlington and knew Mary Anna as they grew up. Two years after graduating from West Point, Lieutenant Lee married Mary Anna Custis at Arlington on June 30, 1831. For 30 years Arlington House was home to the Lees. They spent much of their married life traveling between United States Army duty stations and Arlington, where six of their seven children were born. They shared this home with Mary's parents. After their deaths, Mary's parents were buried not far from the house on land that is now part of Arlington National Cemetery.


text: The Custis family extensively developed the Arlington estate. Much of the steep slope to the east of the house became a cultivated English landscape park, while a large flower garden with an arbor was constructed and planted south of the house. To the west of Arlington House, tall grass and low native plants led down a slope into a natural area of close-growing trees the Custises called "the Grove." About west of the flower garden, "the Grove" contained tall elm and oak trees which formed a canopy. An informal flower garden was planted beneath the trees and maintained by the Custis daughters before 1853.


text: Upon George Washington Parke Custis's death in 1857, he left Arlington Estate to Mary Anna Randolph Custis Lee for her lifetime when it would then go to her eldest son, George Washington Custis Lee. The estate needed much repair and reorganization, and Robert E. Lee, as executor of Custis's will, took a three-year leave of absence from the Army to begin the necessary agricultural and financial improvements.


text: In April 1861, Virginia seceded from the United States. Though offered command of the U.S. Army, Robert E. Lee resigned his commission on April 20,1861 and joined the Confederate States Army. With Arlington House on high ground overlooking the capital, the government of the United States knew it must occupy the mansion or be left in an untenable military position. Although unwilling to leave Arlington House, Mary Custis Lee believed her estate would soon be occupied by federal soldiers and left to stay with relatives on May 14, having been warned by her young cousin William Orton Williams, then serving as aide to General Winfield Scott. Union Army troops seized and occupied Arlington without opposition on May 24.


text: In June 1862, the 37th United States Congress enacted legislation that imposed a property tax on all land in "insurrectionary" areas of the United States. The 1863 amendments to the statute required these taxes to be paid in person. But Mary Lee, afflicted with severe rheumatoid arthritis and behind Confederate lines, could not pay the tax in person. The Arlington estate was seized for nonpayment of taxes. It was auctioned off on January 11, 1864, and the U.S. government won the property for $26,800 ($ today).


text: During the war, Union Army troops cut down many of the trees on the Arlington estate, especially those to the north and east of Arlington House in and near Fort Whipple (north of the house) and Arlington Springs (near the Potomac River). However, a number of large trees remained, particularly those in a forested area (now known as Arlington Woods) west of the house.


text: By early 1864, the military cemeteries of Washington, D.C., and Alexandria, Virginia, were rapidly filling with war dead. Quartermaster General of the United States Army Montgomery C. Meigs proposed using of the Arlington Estate as a cemetery. United States Secretary of War Edwin M. Stanton approved the establishment of a military cemetery on June 15, 1864 and created Arlington National Cemetery. Meigs decided that a large number of burials should occur close to Arlington House to render it unlivable. Officers were to be buried next to the main flower garden south of the house, and the first burial occurred here on May 17. Meigs ordered that additional burials commence immediately on the grounds of Arlington House in mid-June. When Union officers bivouacked in the mansion complained and had the burials temporarily stopped, Meigs countermanded their orders and had another 44 dead officers buried along the southern and eastern sides of the main flower garden within a month.


text: In September 1866, the remains of 2,111 Union and Confederate soldiers who died at the First Battle of Bull Run, Second Battle of Bull Run, and along the Rappahannock River were buried on the former site of "the Grove", southeast of the mansion, beneath the Civil War Unknowns Monument.


text: Robert E. Lee did not visit Arlington after the war. He died as president of Washington College in 1870. Mary Lee died in 1873, having visited the house only one more time, a few months before her death. Too upset at its condition, she refused to enter and left after just a few moments.


text: In April 1874, Robert E. Lee and Mary Custis Lee's eldest son, George Washington Custis Lee, filed suit against the United States government in a Virginia circuit court to regain the property. Custis Lee was a major general in the Civil War and was captured by Union forces at the Battle of Sailor's Creek on April 6, 1865 (see David Dunnels White). A jury found in favor of Custis Lee, leading to extensive appeals by both parties. In 1882, the Supreme Court of the United States ruled in favor of Lee in "United States v. Lee", 106 U. S. 196. The court, by a 5–4 majority, found that the estate had been "illegally confiscated" in 1864 and ordered it returned. But Lee was less interested in obtaining the estate then he was a cash compensation for its value. After several months of difficult negotiations, Lee and the federal government settled on a sale price of $150,000 ($ in dollars). Congress enacted legislation funding the purchase on March 3, 1883; Lee signed over the title on March 31; and the title transfer was recorded on May 14, 1883.


text: In 1920, the Virginia General Assembly changed the name of Alexandria County to Arlington County to end ongoing confusion between Alexandria County and the independent city of Alexandria. The name Arlington was chosen to reflect the presence of the Arlington House.


text: On March 4, 1925, the 68th United States Congress enacted Public Resolution 74, which authorized the restoration of the Lee Mansion in the Arlington National Cemetery, Virginia. The War Department then began to restore Arlington House, and the Department of the Army continues to manage over half of the original plantation's , as Arlington National Cemetery. However, for several years after Congress enacted the authorizing legislation, the War Department, which was responsible for managing the house and grounds, largely ignored the legislation. Contradicting the authorizing legislation, the department, largely at the insistence of Charles Moore, the director of the United States Commission of Fine Arts, furnished and interpreted the Mansion to “the first half of the republic.” This decision was based, in part, on the popularity of the Colonial Revival movement which was still popular in 1925. The Mansion was restored to the period of George Washington Parke Custis, and no furniture manufactured after 1830 was accepted. This approach negated Lee's role and presence at Arlington.


text: In 1955, the 84th United States Congress enacted Public Law 84–107, a joint resolution that designated the manor as the "Custis-Lee Mansion" as a permanent memorial to Robert E. Lee. The resolution directed the United States Secretary of the Interior to erect on the premises a memorial plaque and to correct governmental records to bring them into compliance with the designation, "thus ensuring that the correct interpretation of its history would be applied". Gradually the house was furnished and interpreted to the period of Robert E. Lee as specified in the original legislation. The National Park Service received jurisdiction over the building and some of adjacent gardens (distinguished from the cemetery) beginning June 10, 1933. In 1972, the 92nd United States Congress enacted Public Law 92-333, an Act that amended Public Law 84–107 to designate the manor as "Arlington House, The Robert E. Lee Memorial". In 2017, Members of Congress began writing bills to correct that error and restore the title to Arlington House. Mr. Robert E. Lee never owned Arlington. The owner, his wife is the one who would pay the property taxes. That was his wife's job because she was the owner between her father and her eldest son. He lived there with his wife's parents throughout his Army career.


text: One of the lesser-known histories about Arlington House concerns the Gray family, who helped to preserve the legacy of George Washington Parke Custis as well as the Lee family. Selina Norris Gray, the daughter of Leonard and Sally Norris, was a second-generation Arlington slave. In 1831, Selina married Thornton Gray, a fellow Arlington slave, and eventually had eight children who grew up at Arlington. With the onset of the Civil War, the Lee family had to evacuate their home before the Union troops came and occupied the property. Even though Selina was a personal maid to Mrs. Lee, she and her family were left behind; however, before leaving, Mrs. Lee left the house keys to Selina and the responsibility to protect the treasures of the home. Several of these treasures included cherished family heirlooms that had once belonged to Mrs. Lee's great-grandmother, Martha Custis Washington, and President George Washington.


text: Within months of Union Army General Irvin McDowell occupying the home in 1861, Selina realized that several precious heirlooms were missing due to soldiers looting the property. When she discovered that some of the Washington relics had also disappeared, she promptly provided a list of the missing objects to General McDowell and convinced him that the significance of the collection required his involvement. He first secured the attic and basement areas to prevent further theft, then had the remaining Lee heirlooms shipped to the Patent Office in Washington, D.C., for safekeeping. While Selina is credited with saving the heirlooms and treasures of Arlington House, her children later on are credited with helping to restore the home as well as provide accurate details about the layout of the home, personal stories of the Lee family, and help preservationists in the early twentieth century.


text: During major restorative efforts to Arlington House from 1929 to 1930, the Gray family made another important contribution to the history of Arlington County and the nation. Four of Selina and Thornton's daughters provided crucial details about the house and its furnishings, and their input proved vital to the authenticity of the project. In 2014, the National Park Service acquired a rare photograph of Selina.


text: In 1995, officials of the United States Department of the Interior and the United States Department of the Army signed an agreement to transfer from Arlington House, The Robert E. Lee Memorial, to the Army a part of Arlington Woods, which was located in Section 29 of the NPS at Arlington National Cemetery between Arlington House and Fort Myer. The property transfer, which involved of NPS land, was intended to enable the Cemetery to increase its space for burials.


text: Environmentalists expressed concerns that the agreement would result in the partial destruction of the remnant of a historically important stand of native trees. Nevertheless, Congress enacted legislation in September 1996 authorizing the transfer.


text: On June 5, 2013, after reviewing 100 public comments that it had received on a draft environmental assessment (EA) for the Cemetery expansion project, the United States Army Corps of Engineers released a final EA and a signed Finding of No Significant Impact (FONSI) for the project. The final EA stated that, of the 905 trees to be removed, 771 trees were healthy native trees that had diameters between 6 and 41 inches. The project would remove approximately 211 trees from a less than area containing a portion of a 145-year-old forest that stood within the property boundaries of a historic district that a National Register of Historic Places nomination form for Arlington House had described in 1966. About 491 trees would be removed from an area of trees that was approximately 105 years old. At a public hearing on July 11, 2013, the National Capital Planning Commission approved the site and building plans for the project.


text: From 2003 to 2007, the National Park Service conducted an archeological excavation of two outbuildings that once held Arlington House's slave quarters. In 2009, the Park Service published reports that described the history of the slave quarters and the findings of the excavations, as well as proposals for the restoration of the quarters.


text: From 2007 through 2013, Arlington House underwent its first renovation since 1925. During that period, the National Park Services placed the House's furnishings on display at the Friendship Hill National Historic Site near Point Marion, Pennsylvania. The Park Service held a rededication ceremony after it had completed the renovation and returned the furnishings to the House.


text: Arlington House suffered significant damage in the 2011 Virginia earthquake, requiring the closure of the back halls and upper floor pending an architectural assessment. On July 17, 2014, philanthropist David Rubenstein donated $12.5 million to the National Park Foundation (the arm of the National Park Service which raises funds through private contributions) to rehabilitate Arlington House, its outbuildings, and grounds. The 30-month project is intended to restore the mansion, buildings, and grounds to the way they looked in 1860. The project will repair the earthquake-damaged foundation, and add new interior lighting and a modern climate-control system. National Park Service officials said they are likely to close Arlington House and the slave quarters for several months in 2016, during which most of the work will be done.


text: In 1919, a replica was built for the short-lived Lanier University in Atlanta, designed by architect A. Ten Eyck Brown. It is still standing at 1140 University Drive NE, and houses the Ben H. Zimmerman Religious School and the Canterbury School. Arlington Hall, a two-thirds scale replica of Arlington House, was built in 1939 in Robert E. Lee Park, now Turtle Creek Park, in Dallas, Texas.


text: The façade of the Old Administration Building in Arlington National Cemetery resembles that of Arlington House. The building is west of Arlington House.


title: Gibbs sampling

text: In statistics, Gibbs sampling or a Gibbs sampler is a Markov chain Monte Carlo (MCMC) algorithm for obtaining a sequence of observations which are approximated from a specified multivariate probability distribution, when direct sampling is difficult. This sequence can be used to approximate the joint distribution (e.g., to generate a histogram of the distribution); to approximate the marginal distribution of one of the variables, or some subset of the variables (for example, the unknown parameters or latent variables); or to compute an integral (such as the expected value of one of the variables). Typically, some of the variables correspond to observations whose values are known, and hence do not need to be sampled.


title: Gibbs sampling

text: Gibbs sampling is commonly used as a means of statistical inference, especially Bayesian inference. It is a randomized algorithm (i.e. an algorithm that makes use of random numbers), and is an alternative to deterministic algorithms for statistical inference such as the expectation-maximization algorithm (EM).


title: Gibbs sampling

text: As with other MCMC algorithms, Gibbs sampling generates a Markov chain of samples, each of which is correlated with nearby samples. As a result, care must be taken if independent samples are desired. Generally, samples from the beginning of the chain (the "burn-in period") may not accurately represent the desired distribution and are usually discarded.


title: Gibbs sampling

text: Gibbs sampling is named after the physicist Josiah Willard Gibbs, in reference to an analogy between the sampling algorithm and statistical physics. The algorithm was described by brothers Stuart and Donald Geman in 1984, some eight decades after the death of Gibbs.


title: Gibbs sampling

text: In its basic version, Gibbs sampling is a special case of the Metropolis–Hastings algorithm. However, in its extended versions (see below), it can be considered a general framework for sampling from a large set of variables by sampling each variable (or in some cases, each group of variables) in turn, and can incorporate the Metropolis–Hastings algorithm (or methods such as slice sampling) to implement one or more of the sampling steps.


title: Gibbs sampling

text: Gibbs sampling is applicable when the joint distribution is not known explicitly or is difficult to sample from directly, but the conditional distribution of each variable is known and is easy (or at least, easier) to sample from. The Gibbs sampling algorithm generates an instance from the distribution of each variable in turn, conditional on the current values of the other variables. It can be shown that the sequence of samples constitutes a Markov chain, and the stationary distribution of that Markov chain is just the sought-after joint distribution.


title: Gibbs sampling

text: Gibbs sampling is particularly well-adapted to sampling the posterior distribution of a Bayesian network, since Bayesian networks are typically specified as a collection of conditional distributions.


title: Gibbs sampling

text: Gibbs sampling, in its basic incarnation, is a special case of the Metropolis–Hastings algorithm. The point of Gibbs sampling is that given a multivariate distribution it is simpler to sample from a conditional distribution than to marginalize by integrating over a joint distribution. Suppose we want to obtain formula_1 samples of formula_2 from a joint distribution formula_3. Denote the formula_4th sample by formula_5. We proceed as follows:


title: Gibbs sampling

text: Furthermore, the conditional distribution of one variable given all others is proportional to the joint distribution:


title: Gibbs sampling

text: "Proportional to" in this case means that the denominator is not a function of formula_24 and thus is the same for all values of formula_24; it forms part of the normalization constant for the distribution over formula_24. In practice, to determine the nature of the conditional distribution of a factor formula_24, it is easiest to factor the joint distribution according to the individual conditional distributions defined by the graphical model over the variables, ignore all factors that are not functions of formula_24 (all of which, together with the denominator above, constitute the normalization constant), and then reinstate the normalization constant at the end, as necessary. In practice, this means doing one of three things:


title: Gibbs sampling

text: Gibbs sampling is commonly used for statistical inference (e.g. determining the best value of a parameter, such as determining the number of people likely to shop at a particular store on a given day, the candidate a voter will most likely vote for, etc.). The idea is that observed data is incorporated into the sampling process by creating separate variables for each piece of observed data and fixing the variables in question to their observed values, rather than sampling from those variables. The distribution of the remaining variables is then effectively a posterior distribution conditioned on the observed data.


title: Gibbs sampling

text: The most likely value of a desired parameter (the mode) could then simply be selected by choosing the sample value that occurs most commonly; this is essentially equivalent to maximum a posteriori estimation of a parameter. (Since the parameters are usually continuous, it is often necessary to "bin" the sampled values into one of a finite number of ranges or "bins" in order to get a meaningful estimate of the mode.) More commonly, however, the expected value (mean or average) of the sampled values is chosen; this is a Bayes estimator that takes advantage of the additional data about the entire distribution that is available from Bayesian sampling, whereas a maximization algorithm such as expectation maximization (EM) is capable of only returning a single point from the distribution. For example, for a unimodal distribution the mean (expected value) is usually similar to the mode (most common value), but if the distribution is skewed in one direction, the mean will be moved in that direction, which effectively accounts for the extra probability mass in that direction. (If a distribution is multimodal, the expected value may not return a meaningful point, and any of the modes is typically a better choice.)


title: Gibbs sampling

text: Although some of the variables typically correspond to parameters of interest, others are uninteresting ("nuisance") variables introduced into the model to properly express the relationships among variables. Although the sampled values represent the joint distribution over all variables, the nuisance variables can simply be ignored when computing expected values or modes; this is equivalent to marginalizing over the nuisance variables. When a value for multiple variables is desired, the expected value is simply computed over each variable separately. (When computing the mode, however, all variables must be considered together.)


title: Gibbs sampling

text: Supervised learning, unsupervised learning and semi-supervised learning (aka learning with missing values) can all be handled by simply fixing the values of all variables whose values are known, and sampling from the remainder.


title: Gibbs sampling

text: For observed data, there will be one variable for each observation—rather than, for example, one variable corresponding to the sample mean or sample variance of a set of observations. In fact, there generally will be no variables at all corresponding to concepts such as "sample mean" or "sample variance". Instead, in such a case there will be variables representing the unknown true mean and true variance, and the determination of sample values for these variables results automatically from the operation of the Gibbs sampler.


title: Gibbs sampling

text: Generalized linear models (i.e. variations of linear regression) can sometimes be handled by Gibbs sampling as well. For example, probit regression for determining the probability of a given binary (yes/no) choice, with normally distributed priors placed over the regression coefficients, can be implemented with Gibbs sampling because it is possible to add additional variables and take advantage of conjugacy. However, logistic regression cannot be handled this way. One possibility is to approximate the logistic function with a mixture (typically 7–9) of normal distributions. More commonly, however, Metropolis–Hastings is used instead of Gibbs sampling.


title: Gibbs sampling

text: Suppose that a sample formula_30 is taken from a distribution depending on a parameter vector formula_31 of length formula_32, with prior distribution formula_33. It may be that formula_32 is very large and that numerical integration to find the marginal densities of the formula_35 would be computationally expensive. Then an alternative method of calculating the marginal densities is to create a Markov chain on the space formula_36 by repeating these two steps:


title: Gibbs sampling

text: These steps define a reversible Markov chain with the desired invariant distribution formula_40. This


title: Gibbs sampling

text: can be proved as follows. Define formula_41 if formula_42 for all formula_43 and let formula_44 denote the probability of a jump from formula_45 to formula_46. Then, the transition probabilities are


title: Gibbs sampling

text: since formula_41 is an equivalence relation. Thus the detailed balance equations are satisfied, implying the chain is reversible and it has invariant distribution formula_40.


title: Gibbs sampling

text: In practice, the index formula_51 is not chosen at random, and the chain cycles through the indexes in order. In general this gives a non-stationary Markov process, but each individual step will still be reversible, and the overall process will still have the desired stationary distribution (as long as the chain can access all states under the fixed ordering).


title: Gibbs sampling

text: Let formula_52 denote observations generated from the sampling distribution formula_53 and formula_54 be a prior supported on the parameter space formula_55. Then one of the central goals of the Bayesian statistics is to approximate the posterior density


title: Gibbs sampling

text: To explain the Gibbs sampler, we additionally assume that the parameter space formula_55 is decomposed as


title: Gibbs sampling

text: where formula_61 represents the Cartesian product. Each component parameter space formula_62 can be a set of scalar components, subvectors, or matrices.


title: Gibbs sampling

text: Define a set formula_63 that complements the formula_62. Essential ingredients of the Gibbs sampler is the formula_4-th full conditional posterior distribution for each formula_66


title: Gibbs sampling

text: Note that Gibbs sampler is operated by the iterative Monte Carlo scheme within a cycle. The formula_78 number of samples formula_79 drawn by the above algorithm formulates Markov Chains with the invariant distribution to be the target density formula_80.


title: Gibbs sampling

text: namely, posterior mutual information, posterior differential entropy, and posterior conditional differential entropy, respectively. We can similarly define information theoretic quantities formula_85, formula_86, and formula_87 by interchanging the formula_4 and formula_89 in the defined quantities. Then, the following formula_90 equations hold.


title: Gibbs sampling

text: The mutual information formula_92 quantifies the reduction in uncertainty of random quantity formula_93 once we know formula_94, a posteriori. It vanishes if and only if formula_93 and formula_94 are marginally independent, a posterior. The mutual information formula_97 can be interpreted as the quantity that is transmitted from the formula_4-th step to the formula_99-th step within a single cycle of the Gibbs sampler.


title: Gibbs sampling

text: Numerous variations of the basic Gibbs sampler exist. The goal of these variations is to reduce the autocorrelation between samples sufficiently to overcome any added computational costs.


title: Gibbs sampling

text: In hierarchical Bayesian models with categorical variables, such as latent Dirichlet allocation and various other models used in natural language processing, it is quite common to collapse out the Dirichlet distributions that are typically used as prior distributions over the categorical variables. The result of this collapsing introduces dependencies among all the categorical variables dependent on a given Dirichlet prior, and the joint distribution of these variables after collapsing is a Dirichlet-multinomial distribution. The conditional distribution of a given categorical variable in this distribution, conditioned on the others, assumes an extremely simple form that makes Gibbs sampling even easier than if the collapsing had not been done. The rules are as follows:


title: Gibbs sampling

text: In general, any conjugate prior can be collapsed out, if its only children have distributions conjugate to it. The relevant math is discussed in the article on compound distributions. If there is only one child node, the result will often assume a known distribution. For example, collapsing an inverse-gamma-distributed variance out of a network with a single Gaussian child will yield a Student's t-distribution. (For that matter, collapsing both the mean and variance of a single Gaussian child will still yield a Student's t-distribution, provided both are conjugate, i.e. Gaussian mean, inverse-gamma variance.)


title: Gibbs sampling

text: If there are multiple child nodes, they will all become dependent, as in the Dirichlet-categorical case. The resulting joint distribution will have a closed form that resembles in some ways the compound distribution, although it will have a product of a number of factors, one for each child node, in it.


title: Gibbs sampling

text: In addition, and most importantly, the resulting conditional distribution of one of the child nodes given the others (and also given the parents of the collapsed node(s), but "not" given the children of the child nodes) will have the same density as the posterior predictive distribution of all the remaining child nodes. Furthermore, the posterior predictive distribution has the same density as the basic compound distribution of a single node, although with different parameters. The general formula is given in the article on compound distributions.


title: Gibbs sampling

text: For example, given a Bayes network with a set of conditionally independent identically distributed Gaussian-distributed nodes with conjugate prior distributions placed on the mean and variance, the conditional distribution of one node given the others after compounding out both the mean and variance will be a Student's t-distribution. Similarly, the result of compounding out the gamma prior of a number of Poisson-distributed nodes causes the conditional distribution of one node given the others to assume a negative binomial distribution.


title: Gibbs sampling

text: In these cases where compounding produces a well-known distribution, efficient sampling procedures often exist, and using them will often (although not necessarily) be more efficient than not collapsing, and instead sampling both prior and child nodes separately. However, in the case where the compound distribution is not well-known, it may not be easy to sample from, since it generally will not belong to the exponential family and typically will not be log-concave (which would make it easy to sample using adaptive rejection sampling, since a closed form always exists).


title: Gibbs sampling

text: In the case where the child nodes of the collapsed nodes themselves have children, the conditional distribution of one of these child nodes given all other nodes in the graph will have to take into account the distribution of these second-level children. In particular, the resulting conditional distribution will be proportional to a product of the compound distribution as defined above, and the conditional distributions of all of the child nodes given their parents (but not given their own children). This follows from the fact that the full conditional distribution is proportional to the joint distribution. If the child nodes of the collapsed nodes are continuous, this distribution will generally not be of a known form, and may well be difficult to sample from despite the fact that a closed form can be written, for the same reasons as described above for non-well-known compound distributions. However, in the particular case that the child nodes are discrete, sampling is feasible, regardless of whether the children of these child nodes are continuous or discrete. In fact, the principle involved here is described in fair detail in the article on the Dirichlet-multinomial distribution.


title: Gibbs sampling

text: It is also possible to extend Gibbs sampling in various ways. For example, in the case of variables whose conditional distribution is not easy to sample from, a single iteration of slice sampling or the Metropolis–Hastings algorithm can be used to sample from the variables in question.


title: Gibbs sampling

text: It is also possible to incorporate variables that are not random variables, but whose value is deterministically computed from other variables. Generalized linear models, e.g. logistic regression (aka "maximum entropy models"), can be incorporated in this fashion. (BUGS, for example, allows this type of mixing of models.)


title: Gibbs sampling

text: There are two ways that Gibbs sampling can fail. The first is when there are islands of high-probability states, with no paths between them. For example, consider a probability distribution over 2-bit vectors, where the vectors (0,0) and (1,1) each have probability ½, but the other two vectors (0,1) and (1,0) have probability zero. Gibbs sampling will become trapped in one of the two high-probability vectors, and will never reach the other one. More generally, for any distribution over high-dimensional, real-valued vectors, if two particular elements of the vector are perfectly correlated (or perfectly anti-correlated), those two elements will become stuck, and Gibbs sampling will never be able to change them.


title: Gibbs sampling

text: The second problem can happen even when all states have nonzero probability and there is only a single island of high-probability states. For example, consider a probability distribution over 100-bit vectors, where the all-zeros vector occurs with probability ½, and all other vectors are equally probable, and so have a probability of formula_104 each. If you want to estimate the probability of the zero vector, it would be sufficient to take 100 or 1000 samples from the true distribution. That would very likely give an answer very close to ½. But you would probably have to take more than formula_105 samples from Gibbs sampling to get the same result. No computer could do this in a lifetime.


title: Gibbs sampling

text: This problem occurs no matter how long the burn-in period is. This is because in the true distribution, the zero vector occurs half the time, and those occurrences are randomly mixed in with the nonzero vectors. Even a small sample will see both zero and nonzero vectors. But Gibbs sampling will alternate between returning only the zero vector for long periods (about formula_106 in a row), then only nonzero vectors for long periods (about formula_106 in a row). Thus convergence to the true distribution is extremely slow, requiring much more than formula_106 steps; taking this many steps is not computationally feasible in a reasonable time period. The slow convergence here can be seen as a consequence of the curse of dimensionality.


title: Gibbs sampling

text: A problem like this can be solved by block sampling the entire 100-bit vector at once. (This assumes that the 100-bit vector is part of a larger set of variables. If this vector is the only thing being sampled, then block sampling is equivalent to not doing Gibbs sampling at all, which by hypothesis would be difficult.)


title: Mumbai Central railway station

text: Mumbai Central (formerly Bombay Central, station code: MMCT) is a major railway station on the Western line, situated in Mumbai, Maharashtra in an area known by the same name. It serves as a major stop for both Local and Inter-City/Express trains with separate platforms for them. It is also a terminal for several long-distance trains including the Mumbai Rajdhani Express. It is one of the five major Terminal stations in Mumbai while others being Mumbai CST, Mumbai LTT, Mumbai BDTS and Mumbai Dadar. Trains depart from the station connecting various destinations mostly across states in the northern, western and north-western parts of India. The station was renamed from "Bombay Central" to "Mumbai Central" in 1997, following the change of Bombay to Mumbai. In 2018, a resolution was passed to change the station code to "MMCT", with implementation ongoing.


title: Mumbai Central railway station

text: It was designed by the British architect Claude Batley, and constructed by the Shapoorji Pallonji in 1930 in a record time of 21 months. The project was then costed INR 15.6 million.