the main objective of weather forecasting is to give a robust and reliable prediction of future atmospheric states on the basis of observational data , prior forecasts valid for the initial time of the forecasts and mathematical models describing the dynamical and physical behaviour of the atmosphere .these models numerically solve the set of the hydro - thermodynamic non - linear partial differential equations of the atmosphere and its coupled systems ( like surface or oceans for instance ) .the difficulty with these numerical weather prediction models is that since the atmosphere has a chaotic character the solutions strongly depend on the initial conditions and also on other uncertainties related to the numerical weather prediction process . in practice ,the results of such models are never fully accurate and forecast uncertainties should be also taken into account in the forecast preparation .a possible solution is to run the model with different initial conditions ( since the uncertainties in the initial conditions are one of the most important sources of uncertainty ) and produce an ensemble of forecasts .the forecast ensemble can estimate the probability distribution of future weather variables which allows probabilistic weather forecasting , where not only the future atmospheric states are predicted , but also the related uncertainty information ( which is indeed a valuable extension to the so called deterministic approach , where only the forecast is given without uncertainty estimation ) .the ensemble prediction method was proposed by and since its first operational implementation it has become a widely used technique all over the world and the users understand more and more its merits and economic value as well . however , although e.g. the ensemble mean on average yields better forecasts of a meteorological quantity than any of the individual ensemble members , it is often the case that the ensemble is under - dispersive and in this way , uncalibrated , so that calibration is needed to account for this deficiency .the bayesian model averaging ( bma ) method for post - processing ensembles in order to calibrate them was introduced by .the basic idea of bma is that for each member of the ensemble forecast there is a corresponding conditional probability density function ( pdf ) that can be interpreted as the conditional pdf of the future weather quantity provided the considered forecast is the best one .then the bma predictive pdf of the future weather quantity is the weighted sum of the individual pdfs corresponding to the ensemble members and the weights are based on the relative performance of the ensemble members during a given training period . in practice , the performance of the individual ensemble members should have a clear characteristic ( and not a random one ) or if it is not the case this fact should be taken into account at the calibration process ( see e.g. * ? ? ?* ) . in bma method was successfully applied to obtain 48 hour forecasts of surface temperature and sea level pressure in the north american pacific northwest based on the 5 members of the university of washington mesoscale ensemble .these weather quantities can be modeled by normal distributions , so the predictive pdf is a gaussian mixture .later , developed a discrete - continuous bma model for precipitation forecasting , where the discrete part corresponds to the event of no precipitation , while the cubic root of the precipitation amount ( if it is positive ) is modeled by a gamma distribution . in bma method was used for wind speed forecasting and the component pdfs follow gamma distributions . finally , using von mises distribution to model angular data introduced a bma scheme to predict surface wind direction .  in the present workthe bma method is applied for calibrating ensemble temperature forecasts produced by the operational limited area model ensemble prediction system ( lameps ) of the hungarian meteorological service ( hms ) called aladin - huneps .aladin - huneps covers a large part of continental europe with a horizontal resolution of 12 km and it is obtained by dynamical downscaling ( by the aladin limited area model ) of the global arpege based pearp system of mto france .the ensemble consists of 11 members , 10 initialized from perturbed initial conditions and one control member from the unperturbed analysis .this construction implies that the ensemble contains groups of exchangeable forecasts ( the ensemble members can not be distinguished , thus it is not possible to depict a systematic behaviour of each member ) , so for post - processing one has to use the modification of bma as suggested by .we remark , that bma method has already been successfully applied for wind speed ensemble forecasts of the aladin - huneps in it is shown that bma post - processing of these forecasts significantly improves the calibration and the accuracy of point forecasts as well .now this latter work is extended towards the calibration of the 2 m temperature ensemble forecasts .as it was mentioned in the introduction , bma post - processing of ensemble predictions was applied for temperature data produced by the operational aladin - huneps system of the hms .the data file contains 11 member ensemble ( 10 forecasts started from perturbed initial conditions and one control ) of 42 hour forecasts for 2 m temperature ( given in kelvin ) for 10 major cities in hungary ( miskolc , szombathely , gyr , budapest , debrecen , nyregyhza , nagykanizsa , pcs , kecskemt , szeged ) together with the corresponding validating observations , for the period between october 1 , 2010 and march 25 , 2011 .the forecasts are initialized at 18 utc .the data set is fairly complete , since there are only two days ( 18.10.2010 and 15.02.2011 ) when three ensemble members are missing for all sites and one day ( 20.11.2010 ) when no forecasts are available .figure [ fig : fig1 ] shows the verification rank histogram of the raw ensemble , that is the histogram of ranks of validating observations with respect to the corresponding ensemble forecasts ( see e.g. * ? ? ?* section 8.7.2 ) .it is clear that this histogram is far from the desired uniform distribution , in many cases the ensemble members either underestimate , or overestimate the validating observations ( the ensemble range contains the observed near - surface temperature values only in of the cases ) .hence , the ensemble is under - dispersive and in this way it is uncalibrated . in case of proper calibrationthe probability of a validating observation being below the ensemble range would be and we would have the same probability for the observation being above it . in this way the probability ( i.e. ) can be considered as the nominal value of the ensemble range .in order to calibrate the aladin - huneps ensemble forecasts for temperature the modification of bma normal model of for ensembles with exchangeable members was used .the grouping of ensemble members was similar to the case of wind speed investigated in .in the first model we have two exchangeable groups : one contains the control denoted by  , the other one the 10 ensemble members corresponding to the different perturbed initial conditions which are denoted by  , respectively .we assume that the probability density function ( pdf ) of the forecasted temperature  equals : where  ] we have , while the definition of the pdf  and of the parameters  and   remains the same as for the model .obviously , both the weights and the parameters can be estimated in the same way as before .  to 9 truecm ( a ) ( b )  to 9 truecm ( c ) ( d )  similarly to the two - group case , we also investigate model with additive bias correction ( ) and without bias correction at all (  and  ). we also remark , that according to our experiments with the current data set , the use of different variance parameters for the different groups in models and does not lead to a significant improvement in the performance of the corresponding forecasts .  as an illustration we consider the data and forecasts for debrecen for two different dates 24.11.2010 and 21.12.2010 illustrating two typical situations for models and with linear bias correction .figures [ fig : fig3]a and [ fig : fig3]b show the pdfs of the two groups in model , the overall pdfs , the median forecasts , the verifying observations , the first and last deciles and the ensemble members . the same functions and quantities can be seen in figures [ fig : fig3]c and [ fig : fig3]d , where in addition to the overall pdf we have the three component pdfs and three groups of ensemble members .on 24.11.2010 the spread of the ensemble members is reasonable ( the ensemble range equals 3.3 k ) but all ensemble members underestimate the validating observation ( 279.9 k ) .obviously the same holds for the ensemble median ( 276.9 k ) , while bma median forecasts corresponding to the two- and three - group models ( 279.8 k and 280.0 k , respectively ) are quite close to the true temperature .a different situation is illustrated on figures [ fig : fig3]b and [ fig : fig3]d , where the ensemble range is only 1.4 k , but it contains the validating observation ( 274.3 k ) . the ensemble median ( 273.5 k ) slightly underestimates the true temperature , but the bma post - processing yields more accurate estimators also in this case .the median forecasts corresponding to models and are 273.8 k and 273.7 k , respectively .  in order to check the performance of probabilistic forecasts based on models and and the corresponding point forecasts , as a reference we use the ensemble mean and the ensemble median .we compare the mean absolute error ( mae ) and the root mean square error ( rmse ) of these point forecasts and also the mean continuous ranked probability score ( crps ) and the coverage and average width of central prediction intervals of the bma predictive probability distributions and of the raw ensemble .the coverage of this central prediction interval allows a direct comparison to the raw ensemble , where the ensemble of forecasts corresponding to a given location and time is considered as a statistical sample and the sample quantiles are calculated according to ( * ? ? ?* definition 7 ) .we remark that for mae and rmse the optimal point forecasts are the median and the mean , respectively .further , given a cumulative distribution function ( cdf )  and a real number  , the crps is defined as the mean crps of a probability forecast is the average of the crps values of the predictive cdfs and corresponding validating observations taken over all locations and time points considered .for the raw ensemble the empirical cdf of the ensemble replaces the predictive cdf .the coverage of a  central prediction interval is the proportion of validating observations located between the lower and upper  quantiles of the predictive distribution . for a calibrated predictive pdfthis value should be around  .modeling and analysis of temperature data was performed with the help of the ensemblebma package in r . as a first step the length of the appropriate training periodwas determined , then the performances of the bma post - processed ensemble forecasts corresponding to models and were analyzed .similarly to and to determine the length of the training period to be used we compare the mae values of bma median forecasts , the rmse values of bma mean forecasts , the crps values of bma predictive distributions and the coverages and average widths of bma central prediction intervals for training periods of length  calendar days . in order to ensure the comparability of the results we consider verification results from 02.12.2010 to 25.03.2011 ( 114 days ; being after the maximum training period length ) .consider first the two - group model . in figure[ fig : fig4 ] the crps values of bma predictive distributions , mae values of bma median forecasts and rmse values of bma mean forecasts for different bias correction methods ( black : linear ; blue : additive ; red : no bias correction ) are plotted against the length of the training period .first of all it is noticeable that the results are very consistent for each diagnostics , i.e. the curves are similar for all measures .the best verification scores are obtained without any bias correction : the crps , mae and rmse values are rather constant ( on low values ) with respect to the length of the training period , their relative standard deviations are , and , respectively . in case of linear bias correctionthe values of all diagnostics are decreasing with the increase of the length of the training period reaching their minima around the 3235 days interval ( there is an increase afterwards ) .particularly , crps , mae and rmse take their minima at day 33 , the corresponding values are , and , respectively . for additive bias correctionthe patterns of the curves are very similar to that of the linear case .the minima of crps ( ) and rmse ( ) are also reached at 33 days , while mae takes its minimum of at 34 days ( the value at day 33 is very near to this minimum , in fact that is the second smallest one ) .furthermore , figure [ fig : fig5 ] shows the average width and coverage of the central prediction interval for different bias correction methods as a function of the training period length . concerning the average width the worst results ( largest values )are obtained for model without bias correction and , similarly to the previous diagnostics , the curve is rather flat .the linear bias correction results in the narrowest prediction intervals , the average width is increasing until around 50 days , then shows a slight decreasing trend , so up to 48 days , shorter training periods yield sharper estimates .a similar behaviour can be observed in the case of additive bias correction ( the maximum is reached at around 40 days ) .as far as the coverage values are concerned , unfortunately , none of the considered models result in coverage reaching the nominal value of ( dashed line ). however , the case without bias correction is the best having its maximal value at day 40 with . until that daythe coverage values are slightly increasing and then decreasing afterwards ( although the curve is rather flat again ) .the linear bias correction is starting from the lowest value and reaching its maxima in the period of 3040 days ( actually , the maximum is at day 40 , but the values at these 10 days are very similar ) .the additive bias correction starts higher and reaches its plateau at around day 30 keeping its rather constant values until the end of the examined periods .the maximum coverage values of the two bias corrected cases are slightly below , the additive one being better with a small margin . comparing the average width and coverageit can be noticed that they have opposite behaviour , i.e. the average width values favour shorter training periods , while the coverage figures prefer longer ones. a reasonable compromise should be found , which is at the range of 2040 days .all in all for all three versions of model a 33 days training period seems to be a reasonable choice ( particularly see conclusions based on figure [ fig : fig4 ] , which are not compromised by the other two diagnostics at figure [ fig : fig5 ] ) .the same conclusion can be drawn from figures [ fig : fig6 ] and [ fig : fig7 ] for the variants of the three - group model .the overall behaviour of the different systems for the various diagnostics is very similar to that for the two - group model .the no bias correction option provides the best results all over the time periods in 4 of the 5 diagnostics ( the exception is the average width ) .the additive bias correction slightly outperforms the linear one ( except in terms of average width ) . in terms of specific valuesthe minima for crps , mae and rmse , respectively , are reached again at day 33 for the linear and additive bias corrections . regarding the average widththe values are increasing until day 30 and then they are rather constant until day 50 and decreasing afterwards . for the coverage the period of highest values are between days 30 and 40 ( having another maximum of similar value for the additive bias correction at the end of the period ) .hence , the training period proposed for the two - group model can be kept for the three - group model as well , so we suggest the use of a training period of length 33 days for all the investigated bma models .   according to the results of the previous subsection , to test the performance of bma post - processing on the 11 member aladin - huneps ensemble we use a training period of 33 calendar days . in this wayensemble members , validating observations and bma models are available for the period 04.11.2010 25.03.2011 ( just after the 33 days training period having 141 calendar days , since on 20.11.2010 all ensemble members are missing ) .to get a first insight about the calibration of bma post - processed forecasts we consider probability integral transform ( pit ) histograms .the pit is the value of the predictive cumulative distribution evaluated at the verifying observations , which is providing a good measure about the possible improvements of the under - dispersive character of the raw ensemble .the closer the histogram is to the uniform distribution , the better the calibration is . in figure[ fig : fig8 ] the pit histograms corresponding to all three versions of two- and three - group bma models and are displayed .a comparison to the verification rank histogram of the raw ensemble ( see figure [ fig : fig1 ] ) shows that post - processing significantly improves the statistical calibration of the forecasts .however , in case of linear bias correction both pit histograms are slightly under - dispersive , while for models with additive bias correction and without bias correction one can accept uniformity .the latter statement can be also derived from table [ tab : tab1 ] where the significance levels of kolmogorov - smirnov tests for uniformity of the pit values are listed . based on these testsit can be concluded that the additive bias correction produces the best pit histograms ( the no bias correction case is just slightly worse ) ..significance levels of kolmogorov - smirnov tests for uniformity of pit values corresponding to models and . [ cols="<,^,^,^ " , ]   figure [ fig : fig10 ] shows the bma weights of the control member  in three variants of the two - group model . in case of linear bias correction we have a real mixture in of the forecasted days ( none of the groups has a weight which is almost 1 , e.g. above ) , while for additive bias correction and for model without bias correction this rate equals and , respectively .the values of  that are close to 1 in all three cases correspond to a time interval 18.02.2011 08.03.2011 , when the control member of the ensemble gives much better forecasts than the ten exchangeable ensemble members ( this can be clearly seen from table [ tab : tab4 ] where the mae and rmse values of the particular ensemble members are given for the above mentioned period ) .this special behaviour is therefore correctly diagnosed by the calibration with the provision of large weights for the control member .furthermore , for model with linear bias correction there is a long period between 29.12.2010 and 16.01.2011 where  ( which means that the control is practically not used for the calibration ) , but in the other two cases this phenomenon practically disappears .the average mae and rmse values for that period are also displayed for each ensemble member ( see table [ tab : tab5 ] ) .it can be seen that the control member is not really worse than the other ones ( it outperforms around half of the members ) , which is correctly `` recognized '' by the additive and no bias correction techniques .finally , figure [ fig : fig11 ] shows the bma weights of the control and of the odd and even ensemble members corresponding to the three variants of the three - group model . in case of linear and additive bias correction on a part of the problematic period 18.02.2011 08.03.2011 ( between 20.02.2011 and 05.03.2011 ) the weight  of the control is still close to ( greater than ) , while for the model without bias correction this happens only on four days . in the remaining cases ( , and of the days , respectively ) we have real mixtures of normal distributions ( it is particularly remarkable for the no bias correction ) . on the other hand for the period ,when the control gets zero weight in the linear bias correction it is again ( correctly ) partly disappearing in the additive and no bias correction cases .in the present study the bma ensemble post - processing method is applied to the 11 member aladin - huneps ensemble of the hms to obtain 42 hour calibrated predictions for 2 m temperature .two different bma models are investigated , one assumes two groups of exchangeable members ( control and forecasts from perturbed initial conditions ) , while the other considers three ( control and forecasts from perturbed initial conditions with positive and negative perturbations ) . in both casesthree different treatments of bias are considered ( linear and additive bias correction and no bias correction at all ) and for all models a 33 days training period is suggested .the comparison of the raw ensemble and of the probabilistic forecasts shows that the mean crps values of bma post - processed forecasts are considerably lower than the mean crps of the raw ensemble , while there is no big change in the mae and rmse values of bma point forecasts ( median and mean ) compared to the mae and rmse of the ensemble median and of the ensemble mean .this latter fact might mean that although the spread of the raw ensemble was too small , the median and mean of the point forecasts were sufficiently correct not having too much space for further improvement .it is remarkable to notice that the real probabilistic forecasts as demonstrated by the probability of freezing for debrecen have been significantly improved . for models with additive bias correction and without bias correctionthe coverage of the central prediction interval is rather close to the nominal value , while their pit values fit the uniform distribution . from the six competing post - processing methods the overall performance of the three - group model without bias correction seems to be the best , while models with linear bias correction give the worst results .finally , we conclude that bma post - processing of the aladin - huneps temperature ensemble forecasts significantly improves the calibration and the probabilistic forecasts , however no significant changes are found in accuracy of point forecasts .the first two aspects encourage the operational application of the method , while the third one calls for some further investigations to see whether improvements can be made for the point forecasts as well .  *acknowledgments . *research was supported by the hungarian scientific research fund under grant no .otka nk101680 and by the tmop-4.2.2.c-11/1/konv-2012 - 0001 project .the project has been supported by the european union , co - financed by the european social fund .the authors are indebted to tilmann gneiting for his useful suggestions and remarks and to mt mile and mihly szcs from the hms for providing the data .  99 bao , l. , gneiting , t. , raftery , a. e. , grimit , e. p. and guttorp , p. ( 2010 ) bias correction and bayesian model averaging for ensemble forecasts of surface wind direction . _rev . _ * 138 * , 18111821 .descamps , l. , labadier , c. , joly , a. and nicolau , j. ( 2009 ) ensemble prediction at mto france ( poster introduction by olivier riviere ) _ 31st ewglam and 16th srnwp meetings , _28th september 1st october , 2009 .available at : http://srnwp.met.hu/annual_meetings/2009/download/sept29/morning/posterpearp.pdf  fraley , c. , raftery , a. e. , gneiting , t. and sloughter , j. m. ( 2009 ) ensemblebma : an r package for probabilistic forecasting using ensembles and bayesian model averaging ._ technical report _516r , department of statistics , university of washington .available at : www.stat.washington.edu/research/reports/2008/tr516.pdf         hornyi , a , kertsz , s. , kullmann , l. and radnti , g. ( 2006 ) the arpege / aladin mesoscale numerical modeling system and its application at the hungarian meteorological service ._ i d ojrs _ * 110 * , 203227 .

Abstract: weather forecasting is mostly based on the outputs of deterministic numerical weather forecasting models . multiple runs of these models with different initial conditions result in forecast ensembles which is are used for estimating the distribution of future atmospheric variables . however , these ensembles are usually under - dispersive and uncalibrated , so post - processing is required .  in the present work bayesian model averaging ( bma ) is applied for calibrating ensembles of temperature forecasts produced by the operational limited area model ensemble prediction system of the hungarian meteorological service ( hms ) .   we describe two possible bma models for temperature data of the hms and show that bma post - processing significantly improves calibration and probabilistic forecasts although the accuracy of point forecasts is rather unchanged .  _ key words : _ bayesian model averaging , continuous ranked probability score , ensemble calibration , normal distribution .


one of the most serious challenges in the hunt for transiting extrasolar planets is the removal of the various systematics remaining in the photometric databases even after employing sophisticated methods of ccd image reduction . sometimes called as `` red noise '' , systematics / trends may show up in many ways .their most common appearance is a drift with  d frequency due to variations of the point - spread function and numerous other parameters , for example focus change , sub - pixel coordinate drifts , etc .in addition to these most trivial systematics , we may have many others , from transients ( e.g. , imperfect removal of cosmic rays ) to periodic saturation of bright stars , depending on moon phase . during the past several yearsit has been realized that , except for the simple , high signal - to - noise ratio cases , filtering out these systematics from the databases is absolutely crucial from the point of view of transit search .therefore , efforts have been taken to devise post processing algorithms that are capable of whitening out the data from the systematics .there are two methods in this field that attracted wider interest .the method sysrem by uses basically an iterative principal component analysis to filter out the most prominent systematics from the data . the trend filtering algorithm ( tfa ) by is a least - squares method that is capable of filtering out nearly arbitrary systematics , assuming that the selected set of templates is `` flavorous '' enough , i.e. , it contains the light curves necessary for the approximation of the type of trend observed in the target .here we present tests on the signal recovery capability of tfa .for completeness , we briefly summarize the basic steps of tfa .first we select a _template set _ of light curves from the photometric database of the field of interest . from these \{ } time series ( sampled in moments of time ), we construct the following filter : the coefficients \{ } for a target \{ } are determined by minimizing the following expression : ^ 2 \hskip 2 mm .\end{aligned}\ ] ] here the function is derived in the following way : [r]{(3)}\ ] ] namely , in the case of period search we assume that the observed signal is dominated by systematics and noise , and therefore , the filter is expected to yield minimum dispersion around the constant signal average .once the signal is identified , we can recover its shape by iteratively approximating the noiseless and trend - free signal \{}. ( the iteration is indicated by the symbol in eq . ( 3 ) . ) in this iterative process we assume that \{ } can be represented by a low - parameter model , and that the observed signal minus the systematics yield the true signal with white noise .the datasets used in this paper are listed in table 1 .we test transit detection efficiency ( tde ) , false alarm probability ( fap ) and signal reconstruction capability ( src ) .for testing src on datasets different from those of hatnet , we use the hat - p-1 observations by the 60/90/180 cm schmidt telescope of the konkoly observatory .  to show that tfa is capable of filtering out nearly all systematics , we compute the distribution function of the peak frequencies obtained by the bls analysis . the result of this analysis for field # 125is shown in fig . 1 .we see that the original data includes many stars with various periodic systematics , some of which are not too easy to relate to the daily change of the observational conditions . for example , the strongest peak at  d is most probably associated with the saturation of the bright stars , because after omitting the first stars , the peak at this frequency becomes less prominent than the ones corresponding to other systematics .lrrrrl set & & & [d ] & i [ mag ] & purpose + hatnet # 125 & & & & & tde , fap + hatnet # 127 & & & & & fap + hatnet # 148 & & & & & src + hat - p-1 , schmidt & & & & & src +  , width=226 ]  , width=226 ]  we have already demonstrated in kovcs et al .( 2005 ) the ability of tfa of detecting shallow transits that are buried in noise and systematics .because the statistics we use have slightly changed from then , here we show the results of tests conducted with the new statistics .we inject a periodic transit signal in the given target from the first stars of field # 125 .then we run a tfa / bls analysis on the target and check if the dsp parameter corresponding to the highest peak in the frequency spectrum exceeds a given limit .the dsp parameter expresses the significance of the dip corresponding to the transit derived from the analysis . in order to exclude binaries with light reflection and gravitational effects, dsp also includes weighting by the most significant fourier component of the out - of - transit variation .when computing dsp , we always use the tfa code in the signal reconstruction mode to get a better estimate on this parameter .properties of the injected signal and the number of detections are listed in table 2 .we note that the synthetic signal has a flat out - of - transit part and a trapeze shape with rather long ingress / egress durations .the condition of detection is given by a cutoff imposed on dsp .the value of this cutoff is large enough to eliminate false alarms ( see sect . 4 ) .we see that there is a highly significant increase in the detection probability due to the application of tfa .this increase is especially striking when the top 500 bright stars are tested .these are the ones that are most seriously affected by systematics related to saturation effects ( see above ) .we note that the detection ratio can be slightly increased ( from % to % ) if we choose templates only from this brighter set of stars .crrc tfa & & & [% ] + 0 & & & + 1 & & & + 0 & & & + 1 & & & +by `` false alarms '' we mean those cases when the detection statistics indicate the presence of a signal , but the probability distribution of the statistics ( derived on pure noise ) shows that the observed value may also occur due to a random event and the probability of this to happen is `` greater than we would like to '' . in assessing fap we resort to direct statistical tests , in which we generate pure gaussian time series on the time base of the observed light curves .we analyze these artificial time series and count the number of cases when dsp exceeds a prescribed limit . in this way we get estimates on faps for a given dataset whentfa and bls are used .the results of the tests are presented in table 3 .several conclusions can be drawn from this table .first of all , as expected , application of tfa introduces correlation in the time series .this increases fap by a substantial amount .second , larger number of data points results in a decrease of fap .third , larger number of templates leads to stronger correlation , and therefore , to an increase of fap .fourth , although increasing the number of data points decreases fap , it is present in a relative high value even for higher dsp cutoff values ( when we already expect a visible sign of the ( fake ) transit in the folded / binned light curve .  in an attempt to reduce fap , the following method is suggested . by using several tfa runs , corresponding to various template numbers , we compute dsp values for the given database . due to the way the template sets are constructed ,these results are expected to be largely independent from each other . in a conservative approach of signal detection, we require the signal to be present in all these runs . in the primary selection of transit candidates we require only that the dip is negative ( i.e. , corresponding to dimming ) and that .the result of this multiple template fap filtering is shown in the lower three lines of table 3 .we see that the method is very effective already with three different tfa runs . for example , even for the sparsely sampled field # 127 , with three or more different tfa runs we can filter out false alarms with a probability better than 99.9% for signals with dsp .lrrrcrrr & & & +  : & 5 & 6 & 7 & & 5 & 6 & 7 + & 68 & 7 & 0 & & 26 & 3 & 1 + a & 827 & 400 & 107 & & 258 & 24 & 2 + b & 856 & 523 & 168 & & 306 & 31 & 6 + c & 842 & 560 & 220 & & 394 & 42 & 3 + d & 890 & 638 & 328 & & 474 & 60 & 5 + ab & 386 & 112 & 9 & & 73 & 2 & 0 + abc & 184 & 38 & 1 & & 25 & 0 & 0 + abcd & 97 & 21 & 1 & & 14 & 0 & 0 +signal reconstruction is an essential ( but optional ) part of signal processing when tfa is used .this is because we do not know _ a priori _ which part of the observed signal comes from the systematics and which one from the true signal ( and all these are coupled with noise ) . without knowing the signal parameters _ a priori _ , we resort to an iterative scheme in reconstructing the true signal ( see also sect . 2 ) .our experiments on the hatnet database show that this reconstruction can be quite successful without making any assumption on the signal shape .once the signal shape is reliably identified , one can proceed by more specific assumptions , e.g. , by using trapeze transit shapes , and thereby further decreasing the number of parameters fitted . to illustrate the efficiency of the tfa reconstruction , we show two examples in fig . 2 .  ] , signal - to - noise ratio ( snr ) of the bls spectrum , dsp , snr of the out - of - transit variation and its peak frequency in the units of the bls frequency . on the right we have : star i d , average magnitude , plotting frequency [ d ] , number of data points , dsp .the reconstruction of hat - p-1 was made without using its nearby companion star ads16402 a. in both cases no assumptions were made on the signal shape .[ tfarec],width=245 ]  ] , signal - to - noise ratio ( snr ) of the bls spectrum , dsp , snr of the out - of - transit variation and its peak frequency in the units of the bls frequency . on the rightwe have : star i d , average magnitude , plotting frequency [ d ] , number of data points , dsp .the reconstruction of hat - p-1 was made without using its nearby companion star ads16402 a. in both cases no assumptions were made on the signal shape .[ tfarec],width=207 ]filtering out systematics from astrophysical time series is nearly mandatory if a survey - type analysis is made with the goal of reaching the theoretical white noise limit of signal detection . in the search for extrasolar transiting planetsthis issue becomes even more highlighted due to the delicacy of the detection .we have shown in this paper that tfa is capable of filtering out various systematics , thereby allowing the detection and a concomitant reconstruction of faint regular ( e.g. , simple- or multi - periodic ) signals .furthermore , by requiring multiple detections in time series filtered by various tfa templates , false alarm probability can be pushed down near to the white noise limit .support for program number hst - hf-01170.01-a to g.  .b. was provided by nasa through a hubble fellowship grant from the space telescope science institute .operation of the hatnet project is funded in part by nasa grant nng04gn74 g .we also acknowledge otka k-60750 .bakos , g.  . , noyes , r. w. , kovcs , g. , et al .2004 , pasp , 116 , 266 bakos , g.  . ,noyes , r. w. , kovcs , g. , et al ., 2006 , apj , ( in press ) , ( astro - ph/0609369 ) kovcs , g. & bakos , g.  .2005 , poster paper ( astro - ph/0508081 ) kovcs , g. , bakos , g.  ., & noyes , r. w. 2005 , mnras , 356 , 557 kovcs , g. , zucker , s. & mazeh , t. 2002 , a&a , 391 , 369 kruszewski a. , semeniuk i. 2003 , acta astr . , 53 , 241 pont , f. , zucker , s. , & queloz , d. 2006 , mnras , 373 , 231 tamuz , o. , mazeh , t. , & zucker 2005 , mnras , 356 , 1466

Abstract: we present additional tests of our algorithm aimed at filtering out systematics due to data reduction and instrumental imperfections in time series obtained by ensemble photometry . signal detection efficiency is demonstrated , and a method of decreasing the false alarm probability is presented . including the recently discovered transiting extrasolar planet hat - p-1 , we show various examples on the signal reconstruction capability of the method .


this paper studies incentive schemes to sustain cooperation among self - interested users sharing a common network resource . when users utilize the network resource considering their own self - interest , a problem known as the tragedy of the commons is likely to occur , yielding a suboptimal performance .different methods to overcome the problem have been investigated in the literature .one method widely studied in economics and engineering is pricing .pricing can induce efficient use of network resources by internalizing negative externalities .although pricing has a solid theoretical foundation , implementing a pricing scheme can be impractical or cumbersome in some cases .let us consider a wireless internet service as an example .a service provider can limit access to its network resources by charging an access fee .however , charging an access fee requires a secure and reliable method to process payments , which creates burden on both sides of users and service providers .there also arises the issue of allocative fairness when a service provider charges for the internet service . in the presence of the income effect, pricing will bias the allocation of network resources towards users with high incomes .because the internet can play the role of an information equalizer , it has been argued in a public policy debate that access to the internet should be provided as a public good by a public authority rather than as a private good in a market .another method popular in game theory is to use repeated interaction .repeated interaction can encourage cooperative behavior by adjusting future payoffs depending on current behavior . a repeated game strategy can form a basis of an incentive scheme in which monitoring and punishment burden is decentralized to users ( see , for example , ) .however , implementing a repeated game strategy requires repeated interaction among users , which may not be available .for example , users interacting in a mobile network change frequently in nature .  in this paper, we use an alternative method based on intervention , which was proposed in our previous work . in an incentive scheme based on intervention, a network is augmented with an intervention device that is able to monitor the actions of users and to take an action that affects the payoffs of users . in , we considered an ideal scenario where the intervention device can observe the actions of users without errors immediately after users choose their actions . in this paper , we consider a more realistic scenario where the intervention device can obtain only imperfect information about the actions of users and it takes time for the intervention device to collect signals .intervention directly affects the network usage of users , unlike pricing which uses an outside instrument to affect the payoffs of users .thus , an incentive scheme based on intervention can provide an effective and robust method to induce cooperation in that users can not avoid intervention as long as they use network resources .moreover , it does not require long - term relationship among users , which makes it applicable to networks with a dynamically changing user population .we consider a communication channel shared by users .time is divided into slots of equal length , and in each slot a user can attempt to transmit its packet or wait . if there is only one transmission attempt in a slot , the packet is successfully transmitted .if there is more than one transmission attempt in a slot , packets collide and no transmission is successful . for simplicity , we assume that each user can choose one of two transmission probabilities and , where . note that each user choosing maximizes the total throughput , defined as the average number of successfully transmitted packets per time slot , assuming that all the users choose the same transmission probability .we consider a period consisting of consecutive time slots , and analyze interaction in the period without any consideration of past or future periods .we assume that the number of users and their transmission probabilities are fixed throughout a period .let be the set of the users .the action space of user is denoted by , and the action of user is denoted by , for all .an action profile is represented by a vector .the payoff of user is given by the number of its successfully transmitted packets per time slot .then the expected payoff of user is given by the probability of its successful transmission , .it is easy to see that the action is a dominant strategy for every user .hence , is the unique nash equilibrium , which yields the lower total throughput than the symmetric social optimum .  in order to improve the inefficiency of nash equilibrium, we introduce an intervention device in the system .the intervention device is capable of monitoring the actions of the users and interfering in the transmission of the users .the intervention device can sense the channel to learn whether the channel is idle ( i.e. , no user attempts to transmit its packet ) or busy ( i.e. , at least one user attempts to transmit its packet ) .we consider a scenario where the intervention device collects signals from sensing the channel for the first slots , where , and then chooses its transmission probability , which can be interpreted as the intervention level .let be the set of all possible signals obtained in a slot .then the set of all possible signals that the intervention device can obtain for the slots is .the probability distribution of signals is independent across slots , and when the users choose action profile , the probability of obtaining an idle signal in a slot is given by .after obtaining signals , the intervention device chooses a transmission probability in  ] , and its action is denoted by .the decision rule of the intervention device , called the intervention rule , can be represented by a function .since the transmission probabilities of the users do not change in a period , there is no gain for the intervention device to distinguish signals from different slots .hence , we focus on the class of intervention rules that use only the number of idle signals , which can be represented by .the probability that idle signals arise out of signals when the users choose action profile is , for .note that monitoring is imperfect in the sense that the intervention device can not observe the action profile of the users but obtains only imperfect information about the action profile .the sequence of events in a period can be listed as follows .  at the beginning of the period ,the users choose their transmission probabilities , which are used from slot 1 to slot , knowing the intervention rule adopted by the intervention device .the intervention device collects signals from slot 1 to slot .the intervention device intervenes using the transmission probability prescribed by the intervention rule from slot to slot .the payoff of user when the users choose action profile and the intervention device chooses action is given by the action profile of the users influences the probability distribution of signals , which in turn affects the action of the intervention device .the expected payoff of user when the users choose action profile and the intervention device uses intervention rule can be expressed as a_i \prod_{j \in \mathcal{n } \setminus \{i\ } } ( 1-a_j).\end{aligned}\ ] ] note that can be interpreted as the expected transmission probability of the intervention device , while is the weight on the slots in which the action of the intervention device affects the users .  for notation ,let us define ^k [ 1-(1-p_l)^n]^{t - k},\\ \mu(k;t ) & = \binom{t}{k } [ ( 1-p_l)^{n-1}(1-p_h)]^k [ 1-(1-p_l)^{n-1}(1-p_h)]^{t - k},\end{aligned}\ ] ] for , and let and . is the probability of idle signals arising out of signals when every user cooperates ( i.e. , chooses ) , while is that when exactly one user defects ( i.e. , chooses ) . is the cooperation throughput that each user obtains when all the users choose , while is the defection throughput that a user obtains when it deviates to unilaterally .note that an idle signal is more likely to occur when every user cooperates than when some user defects .also , note that , which reflects the positive gain from defection when there is no intervention .suppose that there is a network manager who determines the intervention rule used by the intervention device .the objective of the manager is to maximize the sum of the payoffs ( i.e. , total throughput ) while sustaining cooperation among the users .the cooperation payoff is given by \tau_c,\end{aligned}\ ] ] while the defection payoff is \tau_d.\end{aligned}\ ] ] hence , the incentive constraint for the users to cooperate can be written as \tau_c \geq \left [ 1 - \frac{t - t}{t } \sum_{k=0}^t \mu(k;t ) f(k ) \right ] \tau_d,\end{aligned}\ ] ] and the problem of designing an intervention rule can be expressed as \tau_c \label{eq : pdp1}\\ & \text{subject to } \left [ 1 - \frac{t - t}{t } \sum_{k=0}^t \lambda(k;t ) f(k ) \right ] \tau_c \geq \left [ 1 - \frac{t - t}{t } \sum_{k=0}^t \mu(k;t ) f(k ) \right ] \tau_d , \label{eq : pdp2}\\ & \qquad \qquad \quad 0 \leq f(k ) \leq 1 \text { for all }.\label{eq : pdp3}\end{aligned}\ ] ]the design problem can be rewritten as a linear programming ( lp ) problem , f(k ) \geq \tau_d - \tau_c \label{eq : lp2}\\ & \qquad \qquad \quad 0 \leq f(k ) \leq 1 \text { for all }.\label{eq : lp3}\end{aligned}\ ] ] the lp problem is to minimize the expected transmission probability of the intervention device while satisfying the incentive constraint and the probability constraints .exerting intervention is necessary to punish a deviation , but at the same time intervention incurs efficiency loss under imperfect monitoring .therefore , the manager wants to use the minimum possible intervention level while providing the incentive for cooperation .the left - hand side of the incentive constraint is the expected loss from deviation due to the change in the probability distribution of signals induced by deviation , while the right - hand side is the gain from deviation .suppose that an optimal solution to the lp problem exists .then the incentive constraint is satisfied with equality at the optimal solution .let be an optimal solution .suppose that \sum_{k=0}^t [ \tau_d \mu(k;t ) - \tau_c \lambda(k;t ) ] f^*(k ) > \tau_d - \tau_c k=\bar{k} k>\bar{k} ] instead of .also , users can have an ability to monitor the actions of other users and the intervention device .in such a scenario , we can study intervention rules to sustain a cooperative decision rule , where a decision rule for a user is a mapping from its information set to its action space .second , the set of signals that the intervention device can obtain in a slot can be generalized .for example , a signal can be ternary ( idle , success , collision ) or the number of users that attempted to transmit .we can investigate how optimal intervention rules and their performance change as the intervention device obtains finer information about the actions of users .finally , we conclude with a remark that incentive schemes based on intervention can be applied to a wide range of networks where cooperative behavior should be encouraged .potential applications include communication networks ( power control , congestion control , and medium access control ) and peer - to - peer networks .

Abstract: we propose an incentive scheme based on intervention to sustain cooperation among self - interested users . in the proposed scheme , an intervention device collects imperfect signals about the actions of the users for a test period , and then chooses the level of intervention that degrades the performance of the network for the remaining time period . we analyze the problems of designing an optimal intervention rule given a test period and choosing an optimal length of the test period . the intervention device can provide the incentive for cooperation by exerting intervention following signals that involve a high likelihood of deviation . increasing the length of the test period has two counteracting effects on the performance : it improves the quality of signals , but at the same time it weakens the incentive for cooperation due to increased delay .


modern astronomical data often consists of 2 high - resolution dimensions : e.g. , \{ } for 2d sky images , \{ } for spectral images as from a long - slit ( or slitless ) spectrometer , and \{ } for time - resolved spectroscopy .there is also a growing body of 3d or 4d data sets , \{ $ ] } , being produced by instruments across the spectrum ( emsellem 2008 ) .here we focus on the needs of the high - energy transmission grating ( hetg ) spectrometer on _ chandra _ ( canizares et al . 2005 ) : a slitless dispersive imaging spectrometer operating in the x - ray range of 0.3 to 8 kev , although the techniques and software ( s / w ) described here are applicable to other instruments as well .  for extended sources observed with the hetg ,the dispersed data are 2d and combine spatial and spectral information ( dewey 2002 ) . a block diagram of the event-2d system used to analyze these data is shown in figure [ pa.11-fig-1 ] .some key ingredients are : the ability to model the 3d geometric - spectral properties of the source , appropriate instrument simulation to generate modeled 2d events from the source photons , the management and viewing of multiple 2d data sets , and a flexible and quantitative comparison of the real and modeled data .event-2d is written in s - lang ( ) , a high - performance interpreted language which is also used in our general x - ray analysis system , isis ( houck & denicola 2000 ) .s - lang / isis allows us to import ( interface to ) a wide variety of external modules ( gsl , volpack , etc . ) in order to extend available functionality ( noble & nowak 2008 ) .this hetg s / w falls under the large umbrella of the hydra ( ) project at mit .the following sections summarize the status of the main components of the current event-2d system .the source-3d s / w allows models to be created as a combination of geometric components each having their own 3d geometry , spectral emission , and velocity properties .examples of some of the geometric primitives provided by the v3d library are shown in figure [ pa.11-fig-2 ] .the v3d routines generate 3d arrays ( data cubes ) of values which can be combined , e.g. , through union and intersection , to produce more complex geometries .the emission spectra associated with each component can be defined by the usual isis function specifications and `` .par '' files .velocity properties including `` hubble - like '' expansion and orbital rotation can be included in the components ; these source motions are very important for the spectral imprints they leave via doppler shifts .the user specification of a source model is most conveniently done through a custom s - lang script file which includes definition of the model parameters and rules for updating the model based on the parameters .while this does require some `` programming '' on the users part , it is relatively simple and gives complete control of the model definition to the user : e.g. , direct access to the structures that define the spectral and the geometric components .the source can include a foreground absorption component which is applied in the observer s rest frame , along with an optional instrument effective area ( or first approximation thereof ) allowing the photon monte carlo ( mc ) generation and subsequent detection to be more efficient . besides useful model visualizations ,the main output of the model is the mc generation of `` photons '' with \{ } values ; these can also be used outside of event-2d for other applications , e.g. , as input to an observatory s simulator .data are loaded from _ chandra_ fits event files into internal structures by specifying the 2 desired event tags , e.g. , \{skyx , skyy } or \{,tg_d}. here also , it is convenient to create a user script to load the data sets .several structures keep track of the instrument properties , the event data , and the viewing and binning parameters for each of the loaded data sets . since these structures are user accessible , custom analyses are facilitated .x - ray instrument simulation is done by mc ray - tracing of appropriate fidelity .the instrument knowledge is coarse but useful : an arf specifies effective area vs energy , a 2-gaussian approximates the on - axis psf , and the detector intrinsic energy resolution is specified by a simple equation , .grating simulation includes period variation and cross - dispersion blurs .the appropriate 2 simulated tags are then loaded into the model events for comparison with the data events , figure [ pa.11-fig-1 ] .the data and model can be compared by binning the events in a regular 2d grid ( image ) and calculating the usual of the residuals between them as shown for two cases in figure [ pa.11-fig-3 ] .  the specific feature of the model that is being fit often guides the range and binning size for the comparison .an important aspect of the fitting here is that the mc model itself contains `` noise '' : re - evaluation with the same input parameters does not give the identical model result .this mc noise can be reduced below scientific relevance by `` over simulating '' , generating more events than in the data and scaling appropriately .even so , the fitting has to be noise - aware and noise - tolerant .a modified conjugate gradient fitting method and a markov chain mc method are available ; each of these requires user guidance in the form of providing a `` should make a noticeable difference '' size scale for each of the fitted parameters .canizares , c.r .2005 , , 117 , 1144 .dewey , d. 2002 , in _ high resolution x - ray spectroscopy with xmm - newton and chandra _ , ed .g. branduardi - raymont , 14 .emsellem , e. 2008 , talk at `` gas and stars in galaxies '' , + http://www.eso.org/sci/meetings/gal3d2008/program.html houck , j.c .& denicola , l.a .2000 , , 591 . noble , m.s . & nowak , m.a .2008 , , 120 , 821 .

Abstract: astronomical data generally consists of 2 or more high - resolution axes , e.g. , x , y position on the sky or wavelength and position - along - one - axis ( long - slit spectrometer ) . analyzing these multi - dimension observations requires combining 3d source models ( including velocity effects ) , instrument models , and multi - dimensional data comparison and fitting . a prototype of such a `` beyond xspec '' ( noble & nowak , 2008 ) system is presented here using _ chandra _ imaging and dispersed hetg grating data . techniques used include : monte carlo event generation , chi - squared comparison , conjugate gradient fitting adapted to the monte carlo characteristics , and informative visualizations at each step . these simple baby steps of progress only scratch the surface of the computational potential that is available these days for astronomical analysis .


codex (= cosmic dynamics experiment ) is a concept for an extremely stable , high - resolution optical spectrograph for the european extremely large telescope ( e - elt ) .the science case for codex encompasses a large range of topics , including the search for exo - planets down to earth - like masses , primordial nucleosynthesis and the possible variation of fundamental constants . however , its prime science driver is the exploration of the universal expansion history by detecting and measuring the cosmological redshift drift using qso absorption lines .this is also one of the 9 ` prominent ' science cases chosen by the e - elt science working group to be among the highlights of the entire e - elt science case .a description of the codex project as a whole was given by .the recognition that an ultra - stable , high - efficiency , high - resolution optical spectrograph would not only be an extremely valuable instrument for the e - elt but also for the vlt led to the development of the espresso concept (= echelle spectrograph for precision super stable observations , see l. pasquini s contribution to these proceedings ) .again , there are a large number of applications for such an instrument , as several other contributions to these proceedings have highlighted .hence , there is also a very strong science case for espresso , including e.g. detailed studies of the intergalactic medium and of stellar abundances .however , apart from these scientific drivers , espresso will also fulfil another role : codex will represent a major development in high - resolution optical spectrographs compared to existing instruments such as uves and harps . in order to achieve its science goals codex will have to deliver an exceptional radial velocity accuracy and stability , i.e.  cm s over a timescale of  yr .although the basic design concepts are already in place , several of the sub - systems needed to achieve the codex requirements do not currently exist .however , they will be implemented in espresso for the first time .hence , in many respects espresso will be a codex precursor instrument that will allow us to test and gain experience with the novel aspects of these instruments . herewe will discuss espresso in the context of its codex precursor role , both in a technical sense as well as with respect to the main codex science driver , which we briefly describe next .the discovery from type ia sne that the universal hubble expansion appears to have begun accelerating at a relatively recent epoch , and its profound implications for fundamental physics have sparked an intense interest in the observational exploration of the universe s expansion history .several methods for measuring the hubble parameter already exist but all of them are either geometric in nature or use the dynamics of localised density perturbations .the simplest , cleanest and most direct method of determining the expansion history , however , is to observe the dynamics of the global robertson - walker metric itself .one way to achieve this is by measuring the so - called redshift drift , i.e. the tiny , systematic drift as a function of time in the redshifts of cosmologically distant sources ( fig.[vdot ] ) .this effect is directly caused by the de- or acceleration of the universal expansion and can hence be used to determine its history .a measurement of this effect would be able to provide evidence of the acceleration that is entirely independent of the snia results or any other cosmological observations , and that does not require any cosmological or astrophysical assumptions at all .it would also provide measurements over a redshift range inaccessible by other methods .recently , found that a -m telescope would indeed have the photon collecting power to detect the redshift drift by monitoring the redshifts of qso absorption lines over a timescale of years ( fig .[ vdot ] ) , providing a strong motivation for a codex - like instrument at the e - elt .the uves and harps experiences have allowed us to identify a number of properties that a spectrograph must feature in order to deliver exceptional radial velocity accuracy and long - term stability , including : simultaneous wavelength calibration , a fully passive instrument with zero human access , located inside a vacuum tank which is itself located inside a nested environment in an underground facility that allows progressively more precise temperature and pressure control , and the flux - weighted timing of observations with sub - second precision .temperature control of the ccd will be particularly important , while high system throughput will also be of the essence .some of these concepts are already established .however , two of the most critical aspects are also those requiring the most r&d : light scrambling and wavelength calibration .  at a resolution of a typical pointing accuracy of  arcsec corresponds to an error of  m s necessitating a scrambling gain of in order to reach  cm s accuracy . hence , in addition to any fibre we will require a dedicated scrambling device to ensure that a photon s position on the ccd only depends on its wavelength but not on its position on the entrance aperture .current wavelength calibration sources such as thar lamps and i cells are sub - optimal in several respects , their non - uniformity and lack of long - term stability being among the concerns . however , a new concept for wavelength calibration has recently emerged . a ` laser frequency comb 'system provides a series of uniformly spaced , very narrow lines whose absolute positions are known a priori with a relative precision of ( see a. manescau s contribution ; ) .neither of the two systems above currently exist , but they would be developed for espresso .being able to test and validate them ` on the sky ' would provide valuable experience and input for further improvements .the scientific goals of codex are sufficiently removed from current observational reality to require validation and demonstration of feasibility of all aspects of data handling and analysis .this includes data acquisition strategies ( e.g. minimum and maximum viable exposure times ) , the tracking of ccd distortions , and the accuracy of flat - fielding , sky subtraction and scattered light corrections .the extraction of the cosmological signal from the data will also require testing .issues include how to deal with qso variability and the accuracy of the conversion to the cosmological reference frame .in addition espresso will allow us to determine the currently unknown intrinsic widths of the narrowest metal absorption lines in order to reassess their usefulness for the drift experiment , and to look for any sources of astrophysical noise so far overlooked .data on qsos collected with espresso for other scientific purposes would allow us to address all of the above issues .we estimate that hours of observations of the brightest known qsos would provide an end - to - end system verification , from data acquisition to signal extraction , at the level of  cm s .since espresso will have characteristics similar to those of codex the question arises whether espresso can be used to make a start on the redshift drift experiment .the idea is that since espresso would be available several years before codex data appropriately collected with espresso could serve as a ` zeroth ' epoch measurement , effectively extending the time baseline of the experiment for a few years , thereby improving the final result without delaying it .[ ol_om ] shows the comparison of the cosmological constraints in the - plane expected from a drift experiment using codex only ( coloured ellipses ) and codex + espresso ( solid contour ) , where we have assumed that espresso would take up operation years before codex .evidently the extension of the time baseline by years is not enough to offset the lack of the vlt s photon collecting power compared to the e - elt : the improvement of the constraints is only quite modest , with the lower limit on increasing by per cent .

Abstract: codex and espresso are concepts for ultra - stable , high - resolution spectrographs at the e - elt and vlt , respectively . both instruments are well motivated by distinct sets of science drivers . however , espresso will also be a stepping stone towards codex both in a scientific as well as in a technical sense . here we discuss this role of espresso with respect to one of the most exciting codex science cases , i.e. the dynamical determination of the cosmic expansion history .