text:
\section{Introduction}
\label{intro}

The estimation of change points challenges analysis methods and modeling concepts. Commonly change points are considered
as isolated singularities in a regular background indicating the transition between two regimes governed
by different internal dynamics.
In time series analysts focus on change points in observed data to reveal dynamical properties of the system
under study and to infer on possible correlations between subsystems.
Detecting trend changes within various data sets is under intensive investigation in numerous research disciplines, such as
palaeo-climatology \cite{Trauth_2009,Mudelsee_2005}, ecology \cite{Girardin_2009,Jong_1998},
bioinformatics \cite{Minin_2005, Liu_1999} and economics \cite{Lia_2007,Andrews_1993}.\\
In general, the detection of transition points is adressed via {\bf(i)} regression \cite{Mudelsee_2009} or
{\bf(ii)} spectral analysis methods \cite{Olsen_2008}, {\bf(iii)} Bayesian approaches \cite{Moreno_2005,Lian_2009} or
{\bf(iv)} recurrence network techniques \cite{Donner_2010,Marwan_2009}.\\
In this work we formulate transition points not only in terms of the underlying regular dynamics, but also
as a transition in the heteroscedastic noise level. We use Bayesian inference to produce estimates for all relevant
parameters.
Our signal model is described by a regular mean undergoing a sudden change and a heteroscedastic fluctuation which
undergoes as well a sharp transition at the same time point. Thus, in its simplest form, the observed signal
$\bm{y}$ has a linear trend undergoing a break point $\theta$ at a time point $t_{i} = \theta$.
The posterior density $p(\theta|\bm{y})$ of the change point given the signal enables us to derive the point estimate
$\hat{\theta}$ as the most likely break point and its confidence bounds.
By applying a sliding window, we formally localize the posterior density and the modelling of the subsignals as a linear trend
is valid in first order. Consequently we investigate time series globally and locally for a generalized break point
in the signal's statisitical properties.\\
In comparison to established methods (e.g. {\bf(ii)} multiscale spectral analysis \cite{Olsen_2008}) our technique is not restricted on
a uniform time grid (e.g. as required for filtering methods).
The majority of existing methods require additional approaches to interpret the confidence of the outcome (e.g. {\bf(i)} bootstrapping,
{\bf(ii)} test statistics, {\bf(iv)} introducing measures). Whereas our technique provides the confidence
intervals of the estimates as a byproduct in a natural way. This, for us is actually
the most convincing argument to approach the detection task via Bayesian inference since
besides the parameter estimation on its own, we obtain a degree of belief about our assumed model
and about the uncertainties in the parameters \cite{DAgostini_2003,BatesDebRoy_2004,Gelman}.
Existing techniques addressing Bayesian inference {\bf(iii)} approach on the
one hand the plain localization task of the singularity by treating the remaining model's parameter as hidden \cite{Fearnhead_2006,Downey_2008}.
On the other hand hierarchical Bayesian models are used \cite{Moreno_2005} mainly based on Monte-Carlo-expectation-maximization
(MEMC) algorithms for the estimation process \cite{Liu_1999,Lian_2009}.\\
In contrast, we intend to achieve an insight in the parameter structure of the time series. We intend to detect
multiple change points without enlarging the model's dimensionality, since this increases considerably the computational time.
By addressing the general framework of linear mixed models (LMM) \cite{McCulloch} we are able to
factorize the joint posterior density into a family of parametrized Gaussians. This mirrors the
separation of the linear from the non-linear parts and it simplifies considerably the explicit computation of the marginal distributions.
Our technique will be applied to a hydrological time series of the river Nile, which exhibits a well known change point.

\section{Definition of the model}

In our modeling approach we consider two aspects of change points in a time series. On the one hand, a change point is
commonly associated with a sudden change of local trend in the data. This indicates a transition point between
two regimes governed by two different internal dynamics.
On the other hand we assume that the systematic evolution of the local variability of the data around its average value
undergoes a sudden transition at the change point.
As we will show, both aspects can be combined into a linear mixed model with hyperparameters.
Our formulation allows the separation of the Gaussian from the intrinsic non-linear parts of
the estimation problem, which besides clarifying the structure of the model, speeds up computations considerably.

\subsection{Formulation of the linear mixed model}
\label{lmm}

The simplest type of signal undergoing a change point at time $\theta$ can be expressed as
    \begin{equation}
y(t) = \beta_{0} \,+\, \beta_{1} |\theta - t|_{-} \,+\, \beta_{2} |\theta - t|_{+} \,+\, \xi(t)\,.
    \end{equation}
Here we use the elementary Hockey sticks of first order defined through
    \begin{equation}
     |\theta-t|_{\tiny -}= \left(\zeta^{\theta}_{-}\right) = \begin{cases}& \theta-t \hspace{2mm} \text{if} \hspace{2mm} t \leq \theta \\& 0 \hspace{9mm}  \text{else} \hspace{8mm} \end{cases}, \label{hockey1}
    \end{equation}
and
    \begin{equation}
     |\theta-t|_{\tiny +}= \left(\zeta^{\theta}_{+}\right) = \begin{cases}& \theta-t \hspace{2mm} \text{if} \hspace{2mm} t \geq \theta \\& 0 \hspace{9mm}  \text{else} \hspace{8mm} \end{cases}. \label{hockey2}
    \end{equation}
Natural data series can in general not be modeled by such a simple behavior as given by these functions. Therefore we
add some random fluctuations $\xi$ around the mean behavior. These random fluctuations can be due to measurement
noise as well as to some intrinsic variability, which is not captured by the low dimensional mean dynamics on both sides
of the change point $\theta$. For this fluctuating part of the signal we suppose that its amplitude is
essentially constant around the change point. The intrinsic variability however may, like  the mean behavior of the system itself,
undergo a sudden change  in its evolution of amplitude.
Hence we consider stochastic fluctuations $\xi(t)$ whose amplitudes undergo a transition themselves according to
    \begin{equation}
\mbox{STD} (\xi(t)) = \sigma (1 \,+\, s_{1} |t-\theta|_{-} \,+\, s_{2} |t-\theta|_{+})\,.
    \end{equation}
The scale factor $\sigma$ could be the level of the measurement noise or some background level of the intrinsic
fluctuations, whereas the constants $s_{1,2}$ describe the systematic evolution of the models intrinsic variability
prior and after the change point measured in units of $\sigma$.
Although clearly the fluctuating part may contain coherent parts, we assume that throughout this work,
that the fluctuations are Gaussian random variables, wich at different time points are uncorrelated
    \begin{equation}
\mathbb{E}(\xi(t)\xi(t^\prime)) = 0\,,\quad t\not=t^\prime\,.
    \end{equation}
This clearly is an approximation and its validity can be questioned in concrete applications. However
this assumption  allows us to implement highly efficient algorithms for the estimation of the involved parameters.
From now on we will call this fluctuating part simply ``noise''.
A realization of such a time series is presented in Fig.{\bf\ref{fig:1}}.
    \begin{figure}
        \includegraphics[width=0.5\textwidth]{model_paper_1}
	\caption{Realization of a synthetic time series of $n_{obs}=100$ data points generated by Equ.(\ref{lm}) whereas
                 the mean is parametrized by
                 $F_{\theta}\bm{\beta}= 5 + 0.22\cdot\bm{\zeta}^{\theta}_{-} + 0.08\cdot\bm{\zeta}^{\theta}_{+}$
                 and the deviation is modeled as
                 $\sigma^{2} \Omega_{\theta, \bm{s}}= \left[1.6(1 + 0.2\cdot\bm{\zeta}^{\theta}_{-} + 0.1\cdot\bm{\zeta}^{\theta}_{+})\right]^{2}$.}
	\label{fig:1}
    \end{figure}
Given a data set of $n$ time points $t_i$, $i=1,\dots,n$, the observation vector $\bm{y} =[s(t_i)]^t \in \mathbb{R}^{n}$ can be written
as follows
    \begin{equation}
      \bm{y} = F\bm{\beta} + \bm{\xi}\hspace{2mm}.\label{lm}
    \end{equation}
Here the fixed effect vector $\bm{\beta}= (\beta_{0},\beta_{1},\beta_{2})^{T}\in \mathbb{R}^3$ corresponds to the coefficients of the
linear combination of the Hockey sticks modeling the mean behavior.
The system matrix of the fixed effects, $F \in \mathbb{R}^{n\times 3}$, is then given by the sampling of the Hockey sticks
$\bm{\zeta}^{\theta}_{\pm}$ defined in Equ.(\ref{hockey1},\ref{hockey2}) at the observation points
    \begin{equation}
    F_{\theta} = \left( \begin{array}{ccc} 1 & \hspace{2.5mm} \left(\zeta^{\theta}_{-}\right)_{1} & \hspace{2.5mm} \left(\zeta^{\theta}_{+}\right)_{1}\vspace{1mm}
\\ \vdots & \hspace{2.5mm} \vdots & \hspace{2.5mm} \vdots\vspace{1mm} \\ 1 & \hspace{2.5mm}
\left(\zeta^{\theta}_{-}\right)_{n} & \hspace{2.5mm} \left(\zeta^{\theta}_{+}\right)_{n}\vspace{1mm} \end{array}\right),
\quad \left(\zeta^{\theta}_{\pm}\right)_{i} = \left(\zeta^{\theta}_{-}\right)(t_i)\,.
    \end{equation}
The noise $\bm{\xi}\in \mathbb{R}^n$ is a Gaussian random vector with zero mean and covariance matrix
$\sigma^2\Omega \in \mathbb{R}^{n\times n}$,
    \begin{equation}
     \bm{\xi} \sim \mathcal{N}\left(0,\sigma^{2} \Omega \right). \label{error}
    \end{equation}
The covariance itself is structured noise, which is parametrized by the two slope parameters $\bm{s}=(s_{1},s_{2})$
and the change point $\theta$ itself as
    \begin{equation}
     \left(\Omega_{\theta,s_{1},s_{2}}\right)_{ij} = \left(\left[ 1 + s_{1}\left(\zeta^{\theta}_{-}\right)_{j} + s_{2}\left(\zeta^{\theta}_{+}\right)_{j}\right]^{2}\right)\cdot\delta_{ij}\,. \\ \label{covariancematrix}
    \end{equation}
In conclusion, the probability density of the observations for fixed parameters (i.e. fixed effects, change point,
slope parameters) can be written as
    \begin{equation}
     \bm{y} \sim \mathcal{N}\left(F\hat{\bm{\beta}},\sigma^{2} \Omega\right)\,.
    \end{equation}
The Likelihood function of the parameters given the data can then be written as
    \begin{equation}
     \mathcal{L}(\bm{\beta},\sigma,\bm{s},\theta|\bm{y})= \frac{1}{(2\pi\sigma^{2})^{\frac{n}{2}}\sqrt{|\Omega|}}\,
     e^{-\frac{1}{2\sigma^{2}}(\bm{y} - F\bm{\beta})^T\Omega^{-1} (\bm{y} - F\bm{\beta}) }\,.\label{Likelihood}
    \end{equation}
Note that the functional dependency of $\bm{\beta}$ is a Gaussian density. Clearly in the exponential $\bm{\beta}$
is of a quadratic form and since $\Xi=F^T\Omega^{-1}F$ is positive definite we may write
    \begin{equation}
  \frac{1}{(2\pi\sigma^{2})^{\frac{n}{2}}\sqrt{|\Omega|}}\,  e^{-\frac{\mathcal{R}^2}{2\sigma^2}} \,
     e^{-\frac{1}{2\sigma^{2}}(\bm{\beta} - \bm{\beta^\ast})^T \Xi (\bm{\beta} - \bm{\beta^\ast} ) }\label{Likelihood_clear}
    \end{equation}
where the mode of the Gaussian in $\bm{\beta}$ is the best linear unbiased predictor of the fixed effects (BLUP) \cite{Robinson_1991}
\begin{eqnarray}\label{eq:blup}
    \bm{\beta}^\ast &=& \underset{\bm{\beta} \in \mathbb{R}^3}{\mbox{argmin}} (\bm{y} - F\bm{\beta})^T\Omega^{-1} (\bm{y} - F\bm{\beta}) \nonumber
                         \\ &=& (F^T\Omega^{-1}F)^{-1} F^T \Omega^{-1} \bm{y}
\end{eqnarray}
and the residuum $\mathcal{R}$ measured in the Mahalanobis distance \cite{Mahalanobis_1936}, induced by the covariance matrix $\Omega$, is
\begin{eqnarray}
    \mathcal{R}^2 &=& \min_{\bm{\beta} \in \mathbb{R}^3} (\bm{y} - F\bm{\beta})^T\Omega^{-1} (\bm{y} - F\bm{\beta})\nonumber\\
        &=& (\bm{y} - F\bm{\beta^\ast})^T\Omega^{-1} (\bm{y} - F\bm{\beta^\ast})\,.
\end{eqnarray}
In addition, the profiled Likelihood function $\mathcal{L}(\bm{\beta}^\ast,\sigma,\bm{s},\theta|\bm{y})$ enables us to derive
the profiled Likelihood estimator of the scale parameter $\sigma$
\begin{equation}\label{eq:sigest}
    \hat\sigma^{2} = \frac{\mathcal{R}^2}{n+1}\, ,
\end{equation}
which is auxiliary for the computation of the maximum of the Likelihood function.

\subsection{Bayesian inversion}
\label{inversion}

    \begin{figure*}[t]
      \begin{tabular}{lcr}
       \hspace{-6mm} a)\hspace{-1.3mm} \includegraphics[width=0.34\textwidth]{theta_neu_2a} & \hspace{-3mm} b) \hspace{-2.3mm} \includegraphics[width=0.32\textwidth]{beta0_neu_2b}
       & \hspace{-3mm} c) \hspace{-2.5mm} \includegraphics[width=0.335\textwidth]{scale_neu_2c}
      \end{tabular}
	\caption{Normalized marginal posterior densities for the time series in Fig.~{\bf\ref{fig:1}}.
                 The maxima indicate the most probable estimates of the
		 a) change point $\hat\theta=40.5$, b) fixed effect offset $\hat\beta_{0}=4.40$ and
                 c) scale parameter $\hat\sigma=1.50$. The dashed lines represent the true parameter values of the underlying model.}
	\label{fig:2}
    \end{figure*}

In the light of the Bayesian theorem, we can compute the posterior distribution $p(\bm{\beta}, \sigma, \theta, \bm{s}|\bm{y})$
of the modeling parameters given the data $\bm{y}$  from the Likelihood function
Eq.~(\ref{Likelihood}) by specifying the prior distribution of the parameters $p(\bm{\beta}, \sigma, \theta, \bm{s})$,
which encodes our belief about the parameters prior to any observation.
Since we assume a priori no correlations between the parameters, the joint prior distribution can be factorized into
the independent parts
    \begin{equation}
      p(\bm{\beta}, \sigma, \theta, \bm{s}) =  p(\theta) \cdot p(\bm{s}) \cdot p(\sigma) \cdot p(\bm{\beta})\,.
    \end{equation}
In general, we do not have any a priori knowledge about these  hyperparameters  and thus we shall use flat and
uninformative priors \cite{Raftery_1986,Wahba_1978}
    \begin{equation}
     p(\theta) \sim 1\,,\hspace{2mm} p(\bm{s}) \sim 1 \,,\hspace{2mm} p(\bm\beta) \sim 1\,,
    \end{equation}
For the scale parameter $\sigma$ we assume a Jeffrey's prior \cite{Jeffreys_1946}
    \begin{equation}
     p(\sigma) \sim \frac{1}{\sigma}\,. \label{jeffrey}
    \end{equation}
These statisitical assumptions enable us to compute the posterior density of the system's parameters given the data
$\bm{y}$ as
    \begin{equation}
      p(\bm{\beta}, \sigma, \theta, \bm{s}| \bm{y}) = C \cdot \mathcal{L}(\bm{\beta}, \sigma, \theta, \bm{s}| \bm{y}) \cdot \frac{1}{\sigma}\,. \label{postplain}
    \end{equation}
The normalization constant $C$ ensures that the right hand side actually defines a normalized probability density.
From this expression, various marginal posterior distributions may be obtained by integrating over the parameters
that shall not be considered.
We are mostly interested in the posterior distribution of the possible change point locations $\theta$.
To produce the posterior distribution of this quantity, we have to marginalize out all other variables.
It turns out that all but the integral over the noise slopes $\bm{s}$ may be carried out explicitely.
Thanks to the Gaussian nature of the $\bm{\beta}$ dependency we obtain
   \begin{equation}
     p(\sigma,\theta,\bm{s} | \bm{y}) \sim \frac{\sigma^{1-n}}{\sqrt{|\Omega||F^T\Omega^{-1}F|}} e^{-\frac{1}{2\sigma^{2}}\mathcal{R}^{2}}\label{sigma} \, ,
   \end{equation}
and
   \begin{equation}
     p(\bm{\beta},\theta,\bm{s} | \bm{y}) \sim \frac{\left[(\bm{y} - F\bm{\beta})^T\Omega^{-1} (\bm{y} - F\bm{\beta})\right]^{-\frac{n}{2}} }{\sqrt{|\Omega|}} \label{beta}\, .
   \end{equation}
Further marginalization may be performed to yield
    \begin{eqnarray}
      p(\theta, \bm{s} | \bm{y}) &=&  \int d\sigma d\bm{\beta}\ p(\bm{\beta},\sigma,\theta, \bm{s}| \bm{y})\\
     &=& C^\prime \cdot \frac{\mathcal{R}^{-(n-2)}}{\sqrt{|\Omega||F^T\Omega^{-1}F|}}\,.\label{pthetaslopes}
    \end{eqnarray}
Again $C^\prime$ is a constant, that ensures the normalization of the right hand side to a probability density.
Finally the posterior marginal distribution of $\theta$ can be computed by numeric evaluation of the following integral
    \begin{equation}
p(\theta | \bm{y}) = \int d\bm{s}\ p(\theta, \bm{s} | \bm{y})\,.\label{ptheta}
    \end{equation}
In the same way the numeric $\theta$ integral may be performed to elaborate the posterior information about the
involved slope parameters $\bm{s}$ of the heteroscedastic behavior around the change point
    \begin{equation}
p(\bm{s} | \bm{y}) = \int d\theta\ p(\theta, \bm{s} | \bm{y})\,.\label{pslope}
    \end{equation}

\section{Validation the method}
\label{performance}

In order to validate the method's performance in an idealized setting we use synthetic time series to discuss
its ability to estimate the model's parameters and to elaborate the sensitivity of the estimates to data loss.
We generate the time series via the LMM Equ.(\ref{lm}) and infer on the change point by computing the global marginal
posterior density Equ.(\ref{ptheta}), i.e. over the interval of all possible change point values $\theta$.
The location of the maximum of the marginal posterior density $\left[p(\theta|\bm{y})\right]_{\mbox{max}}$ can be used
as an estimator for the most probable location of a singularity $\hat\theta$.  In case, the data contains more than one
change point, the posterior distribution will exhibit multiple local maxima. This could therefore be used as an indicator
for the existence of secondary change points in the time series. Although a more reasonable way would be to consider
models with multiple change points this approach becomes quickly uncomputable due to exploding dimensionality.
Thus we propose a local kernel based method to be able to apply our single change point model locally to multi change
point data series.

\subsection{Estimation of a single change point}
\label{single}

    \begin{figure*}
      \begin{tabular}{lr}
       a) \includegraphics[width=0.4\textwidth]{beta12_neu_3a} & \hspace{1cm} b)  \includegraphics[width=0.4\textwidth]{slope12_neu_3b}
      \end{tabular}
	\caption{Normalized two dimensional marginal posterior densities for the time series in Fig.{\bf\ref{fig:1}}.
                 The maxima indicate the most probable estimates of the
                 a) fixed effect slopes $(\hat\beta_{1},\hat\beta_{2})=(\,0.206\,,\,0.096\,)$ and b)
                 deviation slope parameters $(\hat s_{1},\hat s_{2})=(\,0.087\,,\,0.167\,)$.
                 Alongside the contour plots are presented the one dimensional projections of the posterior densities.
                 The dashed lines represent the true values of the underlying model.}
	\label{fig:3}
    \end{figure*}
To validate our technique, we apply it to the generated time series of Fig.{\bf\ref{fig:1}} containing a single
change point at $\theta=40$. We compute all relevant two and one dimensional marginal distributions of the
model's parameters using the formulas of the previous section.
The marginal distributions provide Bayesian estimates for the change point $\theta$,
mean behavior $\bm{\beta}$, scale parameter $\sigma$ and heteroscedastic behavior $\bm{s}$ of the data
as the maxima of the one and two dimensional marginal distributions shown in Fig.{\bf\ref{fig:2}}, {\bf\ref{fig:3}}.\\
First note that due to the random nature of the observations, the posterior density too depends randomly on the actual series
of observations. It is therefore not surprizing, that the locations of the maxima of the posterior does
not exactly agree with the true parameter values. However, they are within a certain quantile of the posterior distribution.
We automatically obtain confidence intervals or regions by considering those level intervals or contour-lines,
that enclose a fixed percentage of the total probability. This yields a natural way of uncertainty quantification.\\
The estimated change point $\hat\theta=40.5$ differs only little from the real value $\theta=40.0$ within a
relatively narrow and symmetric confidence interval $[\,35.7\,,\,45.9\,]$ (Fig.{\bf\ref{fig:2}}a). Consequently we achieve
to restrict the location of a probable singularity to a range $<9\%$ of the time grid.
The estimates of the mean behavior are obtained from Fig.{\bf\ref{fig:2}}b, {\bf\ref{fig:3}}a as
$\hat{\bm{\beta}}=(\,4.40\,,\,0.206\,,\,0.096\,)$. The Bayesian estimates reproduce the real
underlying mean model $\bm{\beta}=(\,5.0\,,\,0.22\,,\,0.08\,)$ convincingly. The two dimensional
contour plot of the marginal density $p(\beta_{1},\beta_{2}|\bm{y})$ of the mean slopes
indicate an approximate symmetric confidence area of the most probable slope combinations $(\beta_{1},\beta_{2})$
(red area in Fig.{\bf\ref{fig:3}}a).
The one dimensional projection $p(\beta_{1}|\bm{y})$ reveals a broader confidence interval for the estimation of
$\hat{\beta_{1}}$ compared to $\hat{\beta_{2}}$.
The scale parameter can be estimated as $\hat{\sigma} = 1.50$ from Fig.{\bf\ref{fig:2}}c within the confidence interval
$[\,0.806\,,\,2.84\,]$ unidirectional wider to growing $\sigma$-values and differs little from the true value
$\sigma = 1.60$.
The two dimensional contour plot of the marginal density of the deviation slope parameters $p(s_{1},s_{2}|\bm{y})$
indicate a slight asymmetric confidence area of the most probable slope combinations $(s_{1},s_{2})$
(red area in Fig.{\bf\ref{fig:3}}b). The one dimensional projections $p(s_{1}|\bm{y})$ and $p(s_{2}|\bm{y})$ display
unidirectional wider confidence bounds for the estimates $\hat{s_{1}}=0.087$ to bigger and $\hat{s_{2}}=0.167$ to smaller
parameter values.
\begin{table}[h]
\caption{Estimated model of the synthetic signal of Fig.~{\bf\ref{fig:1}}}
\label{tab:1}
\begin{tabular}{cll}
\hline
\hline\noalign{\smallskip}
parameter \hspace{2mm} & estimate \hspace{2mm} & confidence $\geq95\%$  \\
\noalign{\smallskip}\hline\noalign{\smallskip}
$\hat\theta$ & 40.5 & [$\,$35.7$\,$,$\,$45.9$\,$] \\
$\hat\beta_{0}$ & 4.40 & [$\,$3.00$\,$,$\,$5.75$\,$] \\
$\hat\beta_{1}$ & 0.206 & [$\,$0.035$\,$,$\,$0.390$\,$] \\
$\hat\beta_{2}$ & 0.096 & [$\,$-0.015$\,$,$\,$0.189$\,$] \\
$\hat\sigma$ & 1.50 & [$\,$0.806$\,$,$\,$2.84$\,$] \\
$\hat s_{1}$ & 0.087 & [$\,$0.027$\,$,$\,$0.220$\,$] \\
$\hat s_{2}$ & 0.167 & [$\,$0.050$\,$,$\,$0.380$\,$] \\
\noalign{\smallskip}\hline
\hline
\end{tabular}
\end{table}\\
Thus for our realization, the marginal distributions of the heteroscedastic behavior $(\sigma,s_{1},s_{2})$ indicate a broad range of probable
parameter combinations compared to the mean behavior $\bm\beta$ or the change point $\theta$.
In Tab.{\bf\ref{tab:1}} we summarize our point estimators and $95\%$ confidence intervals for them based on our
analysis.

\subsubsection{Sensitivity to data loss}
\label{sensitivity}

In real data, analysts have to deal with sparse and irregularily sampled data. Our technique does not require an uniform
sampling grid of data points since from the beginning, it employs only the available data.
As a validation for the sensitivity of our method to data loss, we randomly ignore stepwise $0\%$ up to $87,5\%$ of
the time series modeled by a sequence of $n_{obs}=200$ observations. The artifical time series undergo a change point
$\theta = 80$ and are further parametrized by the mean
$F_{\theta}\bm{\beta}= 12 + 0.24\cdot\bm{\zeta}^{\theta}_{-} + 0.02\cdot\bm{\zeta}^{\theta}_{+}$
and the deviation behavior $\sigma^{2} \Omega_{\theta, \bm{s}}= \left[1.2(1 + 0.18\cdot\bm{\zeta}^{\theta}_{-} + 0.04\cdot\bm{\zeta}^{\theta}_{+})\right]^{2}$.
Leaving out randomly a defined percentage of the observations produces time series with random gaps and irregular
sampling steps. For each of these random realizations consisting of $n_{obs}$ data points we compute the posterior
densities $p_{n_{obs}}^{i}(\theta | \bm{y})$ for $i=1,\dots,50$ realizations.\\
The obtained averaged posterior densities $\left<p(\theta | \bm{y})\right>_{n_{obs}}$ in the plane of the sample size $n_{obs}$
are shown in Fig.{\bf\ref{fig:4}}, indicating with their maxima the averaged most probable change points $\hat{\left<\theta\right>}_{n_{obs}}$.
Apparently the mean of the posterior densities differs from the true value, however still within the
width of the distribution. The latter depends invers proportionaly on the square root of the sample size
\begin{equation}
\mbox{width}\left[\left<p(\theta | \bm{y})\right>_{n_{obs}}\right] \propto \frac{1}{\sqrt{n_{obs}}} \hspace{3mm} .
\end{equation}
At large numbers of sampling points $n_{obs}$ the posterior converges towards a delta distribution located at the true
parameter value $\theta=80$. In any case, even for small data sets, as small as $n_{obs}=25$, the non-flatness of the
posterior clearly hints towards the existence of a change point in the time series.
The investigation of the averaged marginal posterior densities in the plane of the remaining parameters reveals
a broadening of the posterior distributions for $n_{obs}<200$, as naturally expected due to information loss in the
sub time series considered in the inference process.\\
Additionally we point out the efficiency of our method to infer on the explicit location of a singularity $\hat\theta_{n_{obs}}^{i}$
for every single time series of the previous setting. In Fig.{\bf\ref{fig:5}} are presented the histograms of the global
point estimators $\hat\theta_{n_{obs}}^{i}$ for every single realization $i=1,\dots,50$.
We observe that the particular global estimators $\hat\theta_{obs}^{i}$ are relatively robust to data loss and enable us
to infer convincingly on the location of the singularity. Even considering only $50\%$ of the full time series, i.e.
$n_{obs}=100$, produces global estimates that lie in the narrow interval $[76.0\,,\,83.5]$, representing $<4\%$ of the
full time grid.\\
However, for such a data-poor situation, local additional, less dominant maxima are likely to appear due to random
fluctuations in the posterior, and more sofisticated techniqes are needed to assess the existence of single or multiple
change points.
One approach to clearify multimodial posterior densities is the computation of local posterior
densities within a sliding window as presented in the following.
    \begin{figure}
        \includegraphics[width=0.5\textwidth]{validation_neu_4}
	\caption{The global maxima of the averaged posterior densities $\left<p(\theta| \bm{y})\right>_{n_{obs}}$
                 converge for increasing number of data points $n_{obs}$ towards a delta distribution located at the true
                 change point value $\theta = 80$.}
	\label{fig:4}
    \end{figure}

\subsubsection{Local posterior density}
\label{localposteriori}

Long data sets are likely to contain more than one change point. So using our model globally may not be justified. However, locally our model
assumption may still be valid. For this reason, we propose the following kernel based local posterior method. In addition this method allows us to treat very long
data sets numerically more efficient since the computation scales with the the third power of the employed data points.
Around each time point $t$ we choose a data window $I_t=[t-\frac{T}{2}, t+\frac{T}{2}]$ of length $T$.
Inside this window, we take as prior distribution for the change point location $p(\theta)$ a flat prior inside
some subinterval of length a:
\begin{equation}
p(\theta)=\begin{cases}\frac{1}{a} &\hspace{1mm}\mbox{for} \hspace{3mm} t-\frac{a}{2}\leq \theta \leq t+\frac{a}{2}\\
                                 0 &\hspace{1mm}\mbox{else} \end{cases}\,,\quad 0<a<T\,.
\end{equation}
We then compute the local posterior $p_t(\theta|\bm{y}_{|I_t})$ around $t$  based on the subseries in the data window
$\bm{y}_{|I_t}$. This yields a posterior distribution of a possible change point within each window under the
assumption that there is actually a singularity within the window. In order to compare different
window locations, we need to quantify the credibility that there is a change point. Therefore we compute the maximum
of the Likelihood within each window
\begin{equation}
f(t)= \underset{\theta\in[t-\frac{1}{a},t+\frac{1}{a}],s_1,s_2 \in \mathbb{R}}{\mbox{max}}\mathcal{L}( \bm{\beta}^\ast, \hat\sigma; \bm{y}_{|I_t}),
\end{equation}
where $\hat\sigma$ and  $\bm{\beta}^\ast$ are the estimators given by Eq.(\ref{eq:sigest}) and (\ref{eq:blup}).
The global distribution of change points $\theta$ given the full time series is then obtained as a weighted superposition
in form of
\begin{equation}
p(\theta|\bm{y}) = C\cdot\int f(t) \, p_t(\theta| \bm{y}_{|I_t}) dt\,,\label{weighting}
\end{equation}
whereas the constant $C$ ensures the normalization to a probability density.
    \begin{figure}
        \includegraphics[width=0.53\textwidth,height=0.35\textwidth]{histo_test_5}
	\caption{Histograms of the global change point estimators $\hat\theta_{obs}^{i}$ for $i=1,\dots,50$ realizations
                 and with respect to
                 $n_{obs}=50,100,150,200$ data points from the setting of Fig.{\bf\ref{fig:4}}.
                 Even for $n_{obs}=100$ nearly all global estimates $\hat\theta^{i}_{100}$ lie in the
                 interval $[76.0\,,\,83.5]$, respectively $<4\%$ of the full time grid.}
	\label{fig:5}
    \end{figure}
In subdata sets with no change point, the credibility of the model fit is very low,
in conclusion the Likelihood maxima is of very small value and local estimates are judged as negligible.
By construction the method works for multiple change points as soon as they are separated by at least one data window.
We demonstrate this by applying our algorithm first on a synthetic single change point time series.
In Fig.{\bf\ref{fig:6}} is shown the sum of the local posterior densities weighted by the maxima of the local
Likelihood (dashed curve). The time series is one realization of the model in the previous Sect.\ref{sensitivity}
for a sequence of $n_{obs}=200$ data points. Supplementary the applied window size $n_{obs} = 50$ and the
sampling grid of the change points $n_{cp} = 30$ are presented for comparison.
The sum of local posterior densities indicates the best model fit for windows covering the real change point $\theta=80$
but is non-zero even between $[100, 121]$ suggesting that a change point model might be suitable for these singularity values as well.\\
A second quantity that may be used to produce relative credibility weights for the windows
is given by the Bayes factor \cite{Raftery_1995}.
Besides the goodness of fit, the complexity of the assumed model has to be taken into account to assess the most
capable model describing the data and thus performing the estimation. Thus we test the hypothesis of no change point,
respectively a linear model $\mathcal{M}_{lin}$, against a change point model $\mathcal{M}_{cp}$ in form of the Bayes factor
    \begin{equation}
     BF(t) = \frac{p\left(\mathcal{M}_{lin}| \bm{y}_{|I_t}\right)}{p\left(\mathcal{M}_{cp}|\bm{y}_{I_t}\right)}\,.
    \end{equation}
    \begin{figure}
        \includegraphics[width=0.48 \textwidth]{localpost_6}
	\caption{Normalized sum of local posterior densities weigted by the local Likelihood maxima (dashed) and with respect to the Bayes factor
                 (solid), computed for sub time series of $n_{sub}=50$ data points
                 and a sampling grid of $n_{cp}=30$ change points.
                 The data is one realization of the time series
                 defined in Sect.\ref{sensitivity} for $n_{obs}=200$ data points.}
	\label{fig:6}
    \end{figure}
The dependency of the Bayes factor on a logarithmic scale is shown in Fig.{\bf\ref{fig:7}} for the artifical time series
of Fig.{\bf\ref{fig:6}}.
The Bayes factor in this test case favors the change point over the linear model for all local  windows, for which
the true change point is in the support of the inner  prior distribution of $\theta$. This local Bayes factor itself
can be used as a diagnostic tool like the Likelihood weighted posterior,
but we may also combine the techniques by using the $BF$ as a window weighting function by setting $f(t)=e^{-BF(t)}$
in Eq.(\ref{weighting}).
In this form Eq.(\ref{weighting}) corresponds therefore essentially to the total probability decomposition of the change point (cp)
    \begin{equation}
        \sum_{\small\mbox{windows}} p(\theta | \mbox{cp in window})\, p(\mbox{cp exists in window})\,.
    \end{equation}
For comparison of both kernel approaches we present in Fig.{\bf\ref{fig:6}} additionally the sum of local posterior densities
weighted by $e^{-BF(t)}$ (solid curve). The distribution weighted with respect to the Bayes factor are non-zero
in the range between $[78,89]$ whereas the one weighted by the maxima of the Likelihood is non-zero in $[78,121]$. The long tail
of the latter hints to less probable change point locations which are automatically rejected in the Bayes factor
weighting.
    \begin{figure}
        \includegraphics[width=0.48\textwidth]{BF_paper_7}
	\caption{Local Bayes factor (squares) obtained for the time series in Fig.{\bf\ref{fig:6}}.
                 The shaded area encloses values whose support for none of the models is
                 substantial (based on \cite{Raftery_1995}). Values underneath this area strongly support a change point against a linear model,
                 and vice versa for values above.}
	\label{fig:7}
    \end{figure}
Furthermore we exemplify the algorithm on a synthetic multi change point time series shown in Fig.{\bf\ref{fig:8}}.
For clarity of presentation we plot the sum of posterior distributions weighted with the plain Bayes factor $BF$.
We are able to infer on the true change point values $(\theta_{1},\theta_{2},\theta_{3})=(40,100,160)$ via the
estimators $(\hat\theta_{1},\hat\theta_{2},\hat\theta_{3})=(38.9,93.0,162.9)$ within their intervals
$([33.9,47.8],[87.5,109.1],[158.9,167.0])$ of about $90\%$ confidence. We obtain these intervals from a more detailed
analysis of the partial sums of local posterior densities weighted by the factor $e^{-BF}$ covering the estimated
singularity locations.\\
    \begin{figure}[b]
	\includegraphics[width=0.48\textwidth]{multiplecp_8}
	\caption{Normalized sum of local posterior densities weighted by the Bayes factor, computed for sub time
                 series of $n_{sub}=50$ data points
                 and a sampling grid of $n_{cp}=30$ change points. The
                 parametrization of the mean is defined as
                 $F\bm{\beta}= 14 + 0.2\cdot\bm{\zeta}^{40}_{-} + 0.1\cdot\bm{\zeta}^{40}_{+} - 0.25\cdot\bm{\zeta}^{100}_{+} + 0.3\cdot\bm{\zeta}^{160}_{+}$
                 and the deviation is modeled as
                 $\sigma^{2} \Omega= \left[1.6(1 + 0.2\cdot\bm{\zeta}^{40}_{-} + 0.03\cdot\bm{\zeta}^{40}_{+} - 0.05\cdot\bm{\zeta}^{100}_{+} + 0.1\cdot\bm{\zeta}^{160}_{+})\right]^{2}$.}
	\label{fig:8}
    \end{figure}
The main advantage of this localization approach even in a single change point context is however the enormous
speedup of the computations. For instance for a time series of $n_{obs}=2000$ data points we pass from a global computation of the
marginalized posterior density in $3h\,41min\,40s$ to
a local one divided into 40 overlapping subdata sets of $n_{sub}=100$ in $7min\,44s$, respectively a speed up of about $95\%$.
This is achieved using Python 2.6.5 on a Supermicro Intel(R) Core(TM)i7 CPU 920 @ 2.68GHz with 12GB RAM.
In the context of complex multiple change point scenarios, as real time series mostly are, the localization approach
of the posterior density $p(\theta|\bm{y})$ combined with the Bayes factor realizes a powerfull tool to scan the data seperately
for single change points, as demonstrated in the following Sect.\ref{Nile}.

\subsection{Annual Nile flow from 1871 to 1970}
\label{Nile}

We demonstrate our technique by applying it on a time series including a known significant change point.
For this purpose we analyze the annual Nile River flow measured at Aswan from 1871 to 1970 \cite{Cobb_1978}.
Several investigation methods have verified a shift in the flow levels starting from the year 1899 \cite{Cobb_1978,
Jong_1998, Downey_2008}. Historical records provide the fact, that this shift is attributed partly to
weather changes and partly to the start of construction work for a new dam at Aswan.
Since we expect a natural behavior of the underlying mean we generalize our previous model to undergo besides
trend changes as well a sharp shift in the mean offset at the singularity $\theta$.
Therefore we modify the system matrix according to
    \begin{equation}
    F_{\theta} = \left( \begin{array}{cccc} \left(\varphi^{\theta}_{-}\right)_{1} & \hspace{2.5mm} \left(\zeta^{\theta}_{-}\right)_{1} & \hspace{2.5mm} \left(\zeta^{\theta}_{+}\right)_{1} & \hspace{2.5mm} \left(\varphi^{\theta}_{+}\right)_{1} \vspace{1mm}
\\ \vdots & \hspace{2.5mm} \vdots & \hspace{2.5mm} \vdots & \hspace{2.5mm} \vdots\vspace{1mm} \\ \left(\varphi^{\theta}_{-}\right)_{n} & \hspace{2.5mm} \left(\zeta^{\theta}_{-}\right)_{n} & \hspace{2.5mm} \left(\zeta^{\theta}_{+}\right)_{n} & \hspace{2.5mm} \left(\varphi^{\theta}_{+}\right)_{n}\vspace{1mm} \end{array}\right)\hspace{2mm} ,
    \end{equation}
whereas we define another type of Hockey sticks $\bm{\varphi}^{\theta}_{-}$ and $\bm{\varphi}^{\theta}_{+}$
referring to Eq.(\ref{hockey1}) and (\ref{hockey2}) not as linear but as constant. The general formulas of the Bayesian inference
remain the same, with these new functions.
First of all we compute the global posterior density $p(\theta, \bm{s} | \bm{y})$ as presented in Eq.(\ref{pthetaslopes}).
By initially guessing a reasonable sampling grid for the change point $\theta$ and the slope parameters $\bm{s}$
from the data, we clearly obtain significant maxima in the posterior projections $p(\theta|\bm{y})$ and $p(\bm{s} | \bm{y})$.
Therefore we adjust the sampling grid to obtain finer posterior structures around the obvious maxima. We estimate the
change point as $\hat\theta = 1898$ within a confidence interval $[1895,1901]$ of over $95\%$.
The slope parameters of the deviation are estimated as $(\hat{s}_{1},\hat{s}_{2}) = (0.0065, -0.0015)$
within the $90\%$ confidence intervals $\hat{s}_{1}$ in $[-0.0190,0.0450]$ and $\hat{s}_{2}$ in $[-0.0065,0.0855]$.\\
Prior the estimators $\hat\theta$ and $\hat{\bm{s}}$ we compute the posterior
projections $p(\bm{\beta}, \theta, \bm{s} | \bm{y})$ and $p(\sigma, \theta, \bm{s} | \bm{y})$ formulated in Eq.(\ref{beta}) and (\ref{sigma}). By minimizing the
sampling grid of $\theta$ and $\bm{s}$ to its confidence intervals we are able to speed up the compuation and to estimate
the remaining parameters $\bm{\beta}$ and $\sigma$. Finally we reveal from the global posterior distribution
the most probable model plotted in Fig.{\bf\ref{fig:9}} and listed in Tab.{\bf\ref{tab:2}}. \\
Additionally we investigate the time series for local singularities by computing the sum of local posterior densities
weighted by the Bayes factor as $e^{-BF}$ (displayed in Fig.{\bf\ref{fig:9}}) for the window sizes $n_{sub}=50a$ of
considered subseries. The change point sampling grid contains $n_{cp}=30a$ in a resolution of $\Delta\theta = 0.5a$.
Since most secondary maxima are $<1\%$
we ignore them and therefore conclude on one global change point at $\hat\theta=1898$ in the interval $[1896,1900]$
of about $90\%$ confidence. Note that we interpret the splitting of the global maximum as an artefact from the high resolution of
the numerical change point sampling $\Delta\theta = 0.5a$.\\
In conclusion, we are able to confirm previous investigation techniques and auxiliary reveal further information from
the parameter space of the multidimensional posterior density of the applied LMM.
    \begin{figure}
	\includegraphics[width=0.5\textwidth]{allparameters_posteriori_9}
	\caption{Annual Nile flow containing a known change point at $\theta = 1899$.
                 The sum of localized posterior densities weighted with respect to the Bayes factor $BF$
                 indicates a change point at $\hat\theta = 1898$ within its confidence
                 interval $[1896,1900]$ of about $90\%$. The estimated underlying model
                 reveals the most dominant transition in the behavior of the mean.}
	\label{fig:9}
    \end{figure}

\section{Conclusions}
\label{conclusions}

\begin{table}
\caption{Estimated model of the annual Nile flux.}
\label{tab:2}
\begin{tabular}{cll}
\hline
\hline\noalign{\smallskip}
parameter \hspace{2mm} & estimate \hspace{2mm} & confidence $\geq90\%$  \\
\noalign{\smallskip}\hline\noalign{\smallskip}
$\hat\theta$ & 1898 & [$\,$1895$\,$,$\,$1901$\,$] \\
$\hat\beta_{0}$ & 1.12 & [$\,$1.01$\,$,$\,$1.22$\,$] \\
$\hat\beta_{1}$ & -0.0013 & [$\,$-0.0082$\,$,$\,$0.0057$\,$] \\
$\hat\beta_{2}$ & 0.0006 & [$\,$-0.0011$\,$,$\,$0.0024$\,$] \\
$\hat\beta_{3}$ & 0.82 & [$\,$0.76$\,$,$\,$0.90$\,$] \\
$\hat\sigma$ & 0.124 & [$\,$0.094$\,$,$\,$0.160$\,$] \\
$\hat s_{1}$ & 0.0065 & [$\,$-0.0190$\,$,$\,$0.0450$\,$] \\
$\hat s_{2}$ & -0.0016 & [$\,$-0.0065$\,$,$\,$0.0855$\,$] \\
\noalign{\smallskip}\hline
\hline
\end{tabular}
\end{table}

We introduce a general method for the detection of trend changes in heteroscedastic time series by describing the
observations as a linear mixed model. The change point is thereby considered as an isolated singularity in a regular
background of a signal, assuming partial linear mean and deviation in the first order approach.
By addressing the framework of linear mixed models we achieve to simplify the explicit computation of the marginal
posterior distributions and thus reduce the computational time considerably.
The formulation of the marginalized posterior densities of the model's parameters enables us to obtain inter alia
the probability density of a change point given the data. Therefore the technique yields an insight in the
parameter space of the underlying model, estimates these parameters and intrinsically provides a
description of their confidence intervals. \\
We elaborate our technique for single change point models by infering on the relevant model parameters and discuss
the sensitivity of the singularity estimator with respect to data loss.
Additionally we present a kernel based approach to investigate more complex time series with multiple change points
by localizing the posterior density and using the Bayes factor as a weighting function.\\
Moreover we apply our algorithm on the annual flow volume of the Nile River at Aswan from 1871 to 1970. We confirm
a well-established transition in the year 1899 by the estimated change point at 1898 within the interval [$\,$1896$\,$,$\,$1900$\,$] of
about $90\%$ confidence. We specify the underlying model and identify the mean as the statistical property undergoing the most
significant transition.\\
We conclude by emphasizing that our algorithm depicts a powerfull tool to estimate the location of transitions in
heteroscedastic time series and to infer on the underlying behavior in a partial linear approach, meanwhile reducing
the computational time.

\section*{Acknowledgments}

We thank M.H. Trauth for fruitful discussions and gratefully acknowledge financial support by DFG
(GRK Nadi and GRK 1364) and the University of Potsdam.

redpajama_set_name: RedPajamaArXiv


text:
Q: Trying to pass maximum number of characters read by scanf through #define I'm trying to pass a number to scanf of how many characters I want to  read from the input stream. However, I can't get it to work.
My code works when I just put the number in the code, but I want to pass the number through #define to change it easily.
This works:
#include <stdio.h>

int main(void)
{
    char tab[11];

    printf("Podaj tekst: ");
    scanf("%10[^\n]", tab);

    printf("%s", tab);
}

This doesn't work (it only gets characters up until first whitespace character):
#include <stdio.h>

#define size 10

int main(void)
{
    char tab[size+1];

    printf("Podaj tekst: ");
    scanf("%size[^\n]", tab);

    printf("%s", tab);
}

It seems strange to me that it doesn't work. Is there any workaround to do what I want (besides using fgets)?

A: You can convert numerals or other text to strings with the preprocessor # operator. This requires using two macros, one to expand the size macro and another to apply the operator:
#define size 10

#define StringifyHelper(x)  #x
#define Stringify(x)        StringifyHelper(x)

...

char tab[size+1];
scanf("%" Stringify(size) "[^\n]", tab);

redpajama_set_name: RedPajamaStackExchange


text:
Filters: Author is Historic American Engineering Record [Clear All Filters]
Historic American Engineering Record. Elkmont Road, Between Little River Road & Elkmont Campground, Gatlinburg, Sevier County, TN. Library of Congress Prints and Photographs Division: Historic American Engineering Record.
Historic American Engineering Record. Elkmont Vehicle Bridge, Spanning Little River at Elkmont Campground, Gatlinburg, Sevier County, TN. Library of Congress Prints and Photographs Division: Historic American Engineering Record.
Historic American Engineering Record. Foothills Parkway, From Chilowee to Walland & from Cosby to I-40, Gatlinburg, Sevier County, TN. Library of Congress Prints and Photographs Division: Historic American Engineering Record.
Historic American Engineering Record. Great Smoky Mountains National Park Roads & Bridges, Deep Creek Road, Between Park Boundary near Bryson City & Deep Creek Campground, Gatlinburg, Sevier County, TN. Historic American Engineering Record.
Historic American Engineering Record. Great Smoky Mountains National Park Roads & Bridges, Little River Road, Between Sugarlands Visitor Center & Townsend Wye, Gatlinburg, Sevier County, TN. Library of Congress Prints and Photographs Division: Historic American Engineering Record.
Historic American Engineering Record. Great Smoky Mountains National Park Roads & Bridges, Roaring Fork Motor Nature Trail, Between Cherokee Orchard Road & U.S. Route 321, Gatlinburg, Sevier County, TN. Historic American Engineering Record.
Historic American Engineering Record. Great Smoky Mountains National Park Roads & Bridges Team Photo. Library of Congress Prints and Photographs Division: Historic American Engineering Record.
Historic American Engineering Record. Great Smoky Mountains National Park Roads & Bridges, The Loop Over Bridge, Newfound Gap Road 8.6 miles from park entrance, Gatlinburg, Sevier County, TN. Historic American Engineering Record.
Historic American Engineering Record. Greenbrier Road, Between U.S. Route 321 & Greenbrier Road, Gatlinburg, Sevier County, TN. Library of Congress Prints and Photographs Division: Historic American Engineering Record.
Historic American Engineering Record. Heintooga Round Bottom Road & Balsam Mountain Road, Between Blue Ridge Parkway & Big Cove Road, Gatlinburg, Sevier County, TN. Library of Congress Prints and Photographs Division: Historic American Engineering Record.
Historic American Engineering Record. Luten Bridges, Gatlinburg, Sevier County, TN. Historic American Engineering Record.
Historic American Engineering Record. Man in Wagon Driving Oxen. Library of Congress Prints and Photographs Division: Historic American Engineering Record.
Historic American Engineering Record. Mingus Flour Mill, Gatlinburg, Sevier County, TN . Library of Congress Prints and Photographs Division: Historic American Engineering Record.
Historic American Engineering Record. Newfound Gap Road, Between Gatlinburg, TN & Cherokee, NC, Gatlinburg, Sevier County, TN. Library of Congress Prints and Photographs Division: Historic American Engineering Record.
Historic American Engineering Record. Northshore Road, 1 mile spur at Fontana Dam & Bryson City to Noland Creek, Gatlinburg, Sevier County, TN. Library of Congress Prints and Photographs Division: Historic American Engineering Record.
Boucher, Jack E., and Historic American Engineering Record. Observation tower atop Clingmans Dome looking SE, portrait. Library of Congress Prints and Photographs Division: Historic American Engineering Record.
Historic American Engineering Record. Oconaluftee Bridge, Spanning Oconaluftee River, Cherokee, Swain County, NC. Library of Congress Prints and Photographs Division: Historic American Engineering Record.
Historic American Engineering Record. Rich Mountain Road, between Cades Cove & Park Boundary at Rich Mountain Gap. Historic American Engineering Record.
Historic American Engineering Record. Smokemont Bridge, Spanning Oconaluftee River at entrance to Smokemont Campground, Gatlinburg, Sevier County, TN. Library of Congress Prints and Photographs Division: Historic American Engineering Record.
Vint, Thomas, and Historic American Engineering Record. White Rock Lookout Tower, On Mount Cammerer near the Appalachian Trail, Cosby, Cocke County, TN. Library of Congress Prints and Photographs Division: Historic American Engineering Record.

redpajama_set_name: RedPajamaCommonCrawl


Kelly Craft is the first woman to serve as U.S. ambassador to Canada. That's great! Unfortunately, the Kentuckian's primary qualification seems to be that she was a Republican fundraiser. In surely unrelated news, her husband, Joe Craft, is a billionaire coal-mining magnate. Together they've dished out millions to Republican candidates over the years. The new ambassador officially assumed her new gig Monday, and to celebrate, Craft sat with the CBC for an interview.
This mirrored October's dire assessment from the U.N. Intergovernmental Panel on Climate Change-compiled by 91 leading scientists from 40 different countries based on more than 6,000 scientific studies conducted by still more scientists-which found human civilization as we know it will be in severe peril by 2040, and that we have 12 years to dramatically change course to avoid that scenario.
The minuscule number of scientists who disagree do not have anywhere near this kind of evidence to call on. Many are employed by fossil-fuel interests-or the think-tank fronts they pay-that have a vested interest in a different conclusion, or at least in muddying the waters so we don't take action. The American Enterprise Institute, a think tank that recently sent someone on Meet The Press to dispute climate science after the Climate Assessment, has received millions from ExxonMobil and once offered scientists $10,000-a-pop to dispute the consensus.
And that is what Craft was doing here. By suggesting Both Sides are equal, she is actually lying-distorting the truth to prevent action to combat the worst effects of climate change, probably because her husband and his colleagues in the coal and oil and other dirty-fuel industries could lose some money. If Both Sides make a good point, why would we take action in accordance with either one? It's all the same! Never mind that many of the people pushing climate denial do not even have advanced degrees in the relevant fields. When the former coal lobbyist now running the Environmental Protection Agency used it to dispute the National Climate Assessment-a report his agency helped author-he did not use peer-reviewed scientific studies. He used a report from right-wing content farm The Daily Caller.
You might recognize Craft's argument because it's the same one favored by the President of the United States. He recently suggested There Are Very Fine Scientists on Both Sides, and is today reportedly set to roll-back "carbon-capture" regulations on new coal power plants. Yes, we are trying to build new coal power plants in 2018, even though coal no longer functions economically-it was vanquished by natural gas, which is cleaner and cheaper-and, of course, the fact that we have 12 years to save civilization as we know it.
This is in line with an earlier Trump initiative to subsidize coal. Again, coal is one of the dirtiest fuels around, and it's now far more expensive to produce than solar power. But executives and their lobbyist still pay Republican campaign bills. The Republican Party is the only major political party in the industrialized world that disputes the scientific consensus.
That Trump's ambassador to Canada shares a taste for anti-science in service to powerful energy interests is no surprise. His current nominee for the Federal Energy Regulatory Commission, Bernard McNamee, says fossil fuels lead to "a clean environment." The EPA chief, as mentioned, is an ex-coal lobbyist. Craft's stance is a particular problem because of the extensive energy-trading relationship between the U.S. and Canada-they're our largest partner-which often takes the form of pipelines, like the Keystone XL, funneling dirty tar-sands oil from Alberta down into the lower 48. The tar sands may be the dirtiest fossil fuel there is.


Sellick Partnership are currently recruiting for an Interim Senior Finance Business Partner for a council in the west midlands.
Experience of working within a council at this level is essential. Please apply now for immediate consideration.


text:
old-article 111646920993599 https://lifestyle.livemint.com story https://lifestyle.livemint.com News /news/talking-point/from-west-bengal-to-west-brom-111646920993599.html
Home > News> Talking Point > From West Bengal to West Brom
From West Bengal to West Brom
A West Bromwich Albion supporter in India on experiencing relegation and competing with the big clubs in the Premier League
/news/talking-point/from-west-bengal-to-west-brom-111646920993599.html 111646920993599 story
Debanjan Banerjee (centre) with Darren Fletcher (left) and Hal Robson-Kanu at the Hawthorns. Adam Fradgley/AMA
By Nitin Sreedhar
LAST PUBLISHED 28.10.2017 | 08:33 AM IST
Debanjan Banerjee, 29, doesn't really have an answer for why he supports West Bromwich Albion (WBA), a club that is currently 13 in the Premier League rankings. Why not one of the big clubs, like Chelsea or Liverpool? Why support a club that starts every Premier League season looking over its shoulder for other relegation candidates?
"It's difficult to explain how West Brom happened to me," Banerjee says. "I started watching football when I was 13. The first West Brom game I saw was against Manchester United in the 2002-03 season, when West Brom had just been promoted. Maybe I had a thing for underdogs or maybe it was the colours because the navy blue and white of West Brom are similar to my school colours."
Originally from Kolkata, Banerjee used to work in Bengaluru as a data scientist with Accenture. He now writes full-time on his blog, Thefootytraveller.com, travelling the world and making documentaries on football fans. He has travelled to most parts of the UK, South-East Asia, Indonesia, Myanmar and Cambodia, talking to football fans.
During his time as a West Bromwich Albion fan, the club generally remained outside the Premier League—until the 2010-11 season. "The first season I watched, 2002-03, we were relegated, then promoted the year after. Then came the 'Great Escape', which has been my greatest moment as a West Bromwich Albion fan," he adds. West Brom started the final day of the 2004-05 season bottom of the table, but they defeated Portsmouth and avoided relegation as results elsewhere went their way.
Late in 2016, one of his blogs went viral, catching the attention of Gurdial Singh, an Indian-origin Albion fan from West Bromwich who now works with the Albion Foundation.
Singh told Banerjee to stay in touch when he travelled to England. When Banerjee arrived in West Bromwich in September 2016, Singh put him in touch with Drew Williams, the media manager at WBA.
"I had no intention of meeting any players because no matter how small a club it is, West Bromwich Albion are still a Premier League club," Banerjee recalls. Williams not only took Banerjee around the Hawthorns before kick-off (they were playing West Ham United), but he also ended up meeting members of the West Brom squad, including Darren Fletcher (who now plays for Stoke City), Gareth McAuley, Jonny Evans, Hal Robson-Kanu and others. "It was an incredible experience. Everything happened so quickly. It was hard for me to process anything; I was in a state of disbelief."
He also met some of the other club legends—including Tony Brown—on a day when West Brom defeated West Ham 4-2. Banerjee even travelled with the away fans in the coming days for a match at Sunderland.
Still, it must be strange being a West Bromwich Albion fan in India, where every second Premier League fan is wearing the colours of a top-six team.
28.10.2017 | 08:33 AM IST
Premier League | West Bromwich Albion | football club | Chelsea | Liverpool | Debanjan Banerjee | soccer | sports | mint-india-wire


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Federal employees enjoy one of the most generous retirement plans in the country. One major part of their benefits—the Federal Employment Retirement System—has the patina of budget neutrality. FERS is financed completely through contributions to ensure that there will not be shortfalls when federal retirees receive their pension. But because of a quirk in the law dating back to 1986, contributions into the system are skewed dramatically against the taxpayer. For every one dollar that is contributed into FERS by the employee, $14 is contributed by the employer, the taxpayer. If employers and employees contributed equally to the fund as is often the case in the private sector, taxpayers would save $114 billion over ten years and $271 billion over twenty—without affecting federal pension benefit payouts.
Financing the federal retirement system is more expensive than it should be.
Federal retirement is funded through an antiquated formula.
Since 1987, federal employees including members of Congress have had the benefit of three guaranteed income payments in their retirement.
This three-legged retirement system is more generous than what most other middle class families receive in retirement, but it is not opulent. It guarantees a comfortable, though not luxurious, retirement for long-term federal employees.
In 1986, Congress enacted FERS to replace a long-standing federal pension program known as CSRS (civil service retirement system). CSRS was more generous to employees than FERS, but with a catch. CSRS recipients did not receive Social Security and they did not contribute to Social Security payroll taxes. In 1983, as part of an effort to shore up the Social Security Trust Fund, new federal employees were placed in a new federal retirement system and they began contributing to Social Security through FICA, the payroll taxes that nearly all employees pay. This was the beginning of FERS.
At the time, lawmakers decided that the new FERS and existing CSRS employees would contribute the exact same amount for their retirement—including FICA contributions. At the time, CSRS employees contributed 7% to their retirement and so did the taxpayer. Because FERS employees would now contribute 6.2% to FICA, the new law limited the employee contribution to FERS to 0.8% of wages. And because Congress required FERS to be completely self-financed, all of the remaining contribution is made by each federal agency for its employees. This works out to 11.2% of federal employee wages, or $14 contributed by the employer for every one dollar that is contributed by the employee.
It is questionable whether there ever needed to be parity between CSRS and FERS workers in the first place, but it is absolutely unnecessary today. Only federal workers employed before 1984 are eligible for CSRS. Four out of every five federal employees today are under FERS and very soon they will all be under FERS. The problem meant to be solved by the parity requirement between CSRS and FERS no longer exists.
Private retirement plans usually split the bill evenly between employers and employees.
Social Security is funded by employers and employees each paying 6.2% of wages into the system. Under private 401(k) programs, employers and employees each make a matching contribution into an individually-directed retirement account.
Federal employees and the government make matching contributions of up to 5% of wages each under the Thrift Savings Plan; most private companies don't match as much.
And while the costs of a traditional defined benefit pension plan such as FERS are often hidden from the employee, the cost is essentially shared. According to the Department of Labor, about 52% of all private sector pension funds (taking into account defined benefit and defined contribution plans) are contributed by the employer and 48% by the employee.
FERS is unnecessarily expensive for taxpayers.
By themselves, neither FERS nor the Thrift Savings Plans differ much from their private sector counterparts. Together, however, they are much more generous than retirement packages offered by comparable private sector employers.
Today, the federal government contributes a total 12.7% of wages to FERS and the Thrift Savings Plan. By comparison, private employers in similar sectors of the economy (e.g., management, professional services, and information businesses) contribute 5.3% of payroll for their workers' retirement as show in the chart below.
This comparison also takes into account the older age of the federal workforce, which is nearing retirement sooner and requires higher pension funding levels.
Over the next ten years, taxpayers will contribute more than $263 billion to fund FERS, which is considerably more than what the federal government spends on college financial aid through Pell grants. Over the next twenty years, taxpayer contributions will reach roughly $626 billion. Employee contributions are miniscule—less than $20 billion over ten years and less than $50 billion over twenty years.
Modernize FERS to make employers and employees equal partners.
If employers and employees were to contribute equally to FERS, taxpayers would save $114 billion over ten years, $271 billion over twenty years, and $702 billion by 2050.
This sends an important message to the public: Congress and Feds will take the first hit.
If we are going to achieve meaningful fiscal discipline, Congress, the White House, and the federal government must take the first step and take the first significant cuts as an example to the rest of the country.
Third Way polling shows that three-fourths of Americans believe that cutting government spending and getting rid of government waste is the key to balancing the federal budget.
Federal employees will still receive fair treatment for a comfortable retirement.
• Receive a yearly pension of $23,100 that increases at CPI minus 1% each year, just as today.
• Receive Social Security payments of approximately $24,000 that increases by CPI, just as today.
• Have a TSP nest egg that would create an annuity of about $20,000 per year, just as today.
This comes out to roughly $67,000 per year, or approximately the entire replacement salary of an employee's most lucrative years on the federal payroll. And that is on top of any private savings or spouse benefits. The only change would be that federal employees would be paying for a greater portion of the funding of their pension.
Taxpayers would save hundreds of billions of dollars.
In 2011, taxpayers will pay roughly $19 billion to fund future federal pensions, while federal employees will contribute just over $1 billion. By 2030, taxpayers will fund close to $38 billion to fund future pensions, while federal employees will contribute about $3 billion.
That is simply unfair to taxpayers and a burden that would never occur in the private sector. If there were contribution parity, the savings would increase from $9 billion in 2011 to $18 billion in 2030 and over $30 billion in 2050.
This will harm federal employees.
Federal employees will definitely pay a price, but only as far as they will have to accept the same arrangement offered to most workers. Pension contributions that were once financed almost exclusively by taxpayers will now be shared equally. That is the way it is done for Social Security, 401k-style retirement programs, and most private pension plans. Federal employees, through a quirk in the law that was meant to solve a problem that no longer exists, have gotten a very generous deal for the last 25 years. It is time for all federal employees to pay their fair share.
This will harm veterans and military retirees.
Not true. This covers only those in FERS—federal employees, congressional employees, members of Congress, and judicial branch employees. Military retirees are covered under a separate program administered by the Department of Defense.
Why didn't you propose a similar change in CSRS financing?
CSRS is financing is already equally shared—7% by the employer and 7% by the employee—so there is no imbalance to rectify. Even if a contribution discrepancy did exist, there haven't been any new CSRS-eligible employees added to the federal workforce on over 20 years. CSRS employees are quickly leaving the system and being replaced by FERS employees. Roughly four-fifths of current federal employees are under FERS and by the end of this decade very few CSRS employees will remain.
Isn't another reason for reforming federal retirement that federal workers are paid more than private sector employees?
No, news reports that claim federal workers are overpaid compared to private workers are misleading. Making apples to apples comparison with the private sector doesn't work because the characteristics of the workforce and the nature of the work are different. Generally, the federal workforce is more highly skilled than the average private employer's workforce. Detailed analysis shows that federal employees' salaries are roughly the same or less than private employees' salaries. To address the controversy, however, the U.S. Office of Personnel Management has recently called for a new analysis of salary comparisons. Such detailed analysis should include a comparison of the financing for federal retirement benefits, which Third Way estimates is more generous than for comparable private workers.
* Federal pension benefits are determined by a simple formula. It equals the average salary of the three most lucrative years of a person's federal employments, multiplied by 1.1% (or 1.0% if the employee works for less than 20 years), and multiplied by the number of years of service. Thus, $70,000 as a "high three" multiplied by 1.1% equals $770 which is multiplied by 30 years for a total of $23,100.
Way and can be reached at dkendall@thirdway.org. The authors would like to thank Jesse McCormick for his research assistance.
Third Way is the leading think tank of the moderate wing of the progressive movement. We work with elected officials, candidates, and advocates to develop and advance the next generation of moderate policy ideas.
For more information about Third Way please visit www.thirdway.org.
Your FERS pension and Social Security will be fixed dollar amounts. But the money you get from your TSP will depend on how much you contributed and how well you managed the money.
As a FERS, you have a chance to take a more active role in managing your own retirement than CSRS do. But, that means you need to stay up-to-date on your benefits.
Your FERS Pension could also be reduced if you choose survivor benefits. Will my survivor still get my pension when I die?
The Thrift Savings Plan (TSP) is a special account for Federal Employees. The TSP was created as part of the Federal Employees Retirement System in 1986. Most government employees (FERS and CSRS) are eligible for the TSP — even those hired before it was created.
The TSP allows you to save pre-tax dollars in a special personal account. You can choose how to invest those dollars — although your choices are limited.
With your FERS retirement pension and Social Security, you will receive fixed amounts. But with your TSP, the amount you receive depends on how much you put in and how well you managed the money.
Your TSP contributions are optional and separate from your FERS pension.
You may also be able to get your Federal Agency [taxpayers] to contribute money to your TSP. Click here to learn more about the match the government gives FERS employees.
Employees covered under the Federal Employee Retirement System (FERS) are typically eligible to receive Social Security benefits when they retire. Every pay period, the Federal Government takes out 6.2% of your basic pay to put towards Social Security. But just like your FERS pension, your Social Security benefit is not based on your contributions - it is based on other factors.
According to the U.S. Social Security Administration, the Social Security taxes you and other workers pay into the system are used to pay for Social Security benefits.
You pay Social Security taxes on your earnings up to a certain amount. That amount increases each year to keep pace with wages. In 2011, that amount is $106,800.
You pay Medicare taxes on all of your wages or net earnings from self-employment. These taxes are used for Medicare coverage.
Currently, U.S. citizens cannot collect Social Security benefits until age 62 (lawmakers are considering raising this age to 67 or 70). The maximum Social Security benefit at age 62 is $21,636 per individual.
* The employee contribution was temporary lowered from 6.2% to 4.2% on January 1, 2011.
There has recently been a flurry of critical columns examining the devastation done to our nation's fiscal health by government workers. Our cities, states, and federal government are in critical condition. Cities have begun declaring bankruptcy, and states such as California and Illinois are tottering. The federal government, which supplied a big chunk of stimulus dollars merely to keep states on life support, is running massive deficits and accumulating debts as far as the eye can see. What caused the problems?
There are two sides of the ledger responsible. Declining state tax receipts (considered "earnings" by government) played a role (the receipts side). But the real scourge has been on the expense side of the ledger: salaries and pension benefits given -- and I do mean given -- to government workers.
"Fully one-third of the 'stimulus' money went to state and local governments -- an obvious payoff to public employee unions that contributed so much to Democrats," as Michael Barone noted.
Public-sector unionism is a very different animal from private-sector unionism. It is not adversarial but collusive. Public-sector unions strive to elect their management, which in turn can extract money from taxpayers to increase wages and benefits -- and can promise pensions that future taxpayers will have to fund.
Obama and the Democrats have been well-rewarded for their patronage. Unions contributed up to 400 million dollars to Democrats in 2008 and engage in skullduggery to advance their aims. The latest revelation: a union-funded slush fund secretly targeting GOP candidates through the use of money-laundering and front groups. Unions have funded all sorts of political activity -- undoubtedly the major reason Obama, in one of his first acts as president, ended union disclosure rules requiring them to report how their members' dues were being spent. So much for transparency.
Franklin Roosevelt, of all people, was alert to the danger of this collusion between politicians and unions. He maintained that "the process of collective bargaining, as usually understood, cannot be transplanted into the public service." Yet it has been transplanted; today, a majority of union workers for the first time work for the government. And the government has brought good things to them.
For most Americans, the Great Recession has been an occasion to hold on for dear life. For public employees, it's been an occasion to let the good times roll.
The New York Times reports that state and local governments have added a net 110,000 jobs since the beginning of the recession, while the private sector has lost 6.9 million.
The gap between total compensation of public and private workers has only widened during the downturn, according to USA Today. In 2008, benefits for public employees grew at a rate three times that of private employees.
The President's new budget can be symbolized by the old wartime poster: Uncle Sam Wants You. Until Barack Obama came into office, the number of federal employees had held relatively constant. But that was so 2008. That number jumped from 1.875 million in 2008 to 1.98 million in 2009, and it looks to jump a farther in 2010 -- a 14.5% leap in two years. (And the boom is in federal agencies, not the military; hiring at the IRS, EPA, and the Justice Department is a big portion of the increase. Big Brother is getting bloated -- maybe we can get Michelle to work on this obesity problem.)These jobs come with munificent salaries and benefits.
The pensions are manipulated upwards and gold-plated, too, as I noted in "Taxpayers: Eat your hearts out, suckers." Many others have begun to notice the drain on public finances by pensions for government workers, and the public pension tsunami has just begun. This is the engine driving our ballooning deficits and public debt. Merely rolling federal employee pay back to where it was in 1998 relative to the private sector, and shifting state and local government pay back to 2005 relative levels, would save $116 billion annually from government costs.
We know this will never happen as long as Democrats are in power. They like this perpetual motion machine. A government bureau, Ronald Reagan quipped, is the nearest thing to eternal life we'll ever see on earth. But we can try, and there is certainly potential for Republicans to seize on this problem as it begins to gain traction in the public mind. The issue seems tailor-made for Tea Partiers.
Meanwhile, Big Brother, like many big brothers, has become a bully. The Internal Revenue Service is on a hiring binge to crack down on taxpayers; fees on candy, plastic bags, iPod downloads, sugar, and many other things that make life fun are going up and up; our tax rates are inflating; and studies show that there has even been an explosion in parking tickets and fines for every picayune sort of "violation" that the bureaucrats can dream up in all their spare time -- phantom taxes, they have been called. The leviathan must be fed.
But even this good deal is not good enough for Barack Obama. He is a very mischievous man whose Modus Operandi is to distract and defame and engage in a great deal of sleight of hand. If he truly is a "sort of God" (as one of his adoring Newsweek pundits characterized him), that God would be Janus of two faces. While he talks the talk about the deficit and freezing discretionary spending, Obama engages in a spending binge that would make Imelda Marcos proud. But look what else the Magician-in-Chief is doing: giving even more money and benefits to government workers, and doing it in a very untransparent and sneaky way.
Barack Obama is planning a major overhaul of the Federal government pay system that would boost pay for government workers while loosening scrutiny on how they do their jobs. When he released his budget, there was a section titled "Improving the Federal Workforce." Sounds good, right? But watch what the man and his minions do, not what they say.
But then comes the trickery, disguised as "reform" and "refreshing" the system. This team is addicted to euphemisms (and their thesauruses are well-thumbed).
Berry mused about eliminating the first two ranks of the 15-grade GS system and adding grades 16 and 17. Berry did not explicitly advocate a pay raise for federal workers during the interview, but those in the added grades presumably would be paid more than the current top rate.
"I'm a strong proponent of breaking the chain to the desk and breaking the chain to the time clock," he said. He wants government to "move in a direction to empower and trust our employees to get the job done ... and not focus so much on where they're sitting and what hours they're sitting there."
Does that sound like a plan to increase efficiency of government workers? Give them higher pay, but allow them to set their own hours and work from...where? Starbucks? Home? The zoo?
And how is this "reform" going to happen? Are the people or our representatives going to have a say in how our money is spent? Need one ask?
The plans are in the final stages and will be put in place by a presidential memorandum or executive order. In other words, they'll be implemented by presidential fiat. This is the form of government we have now -- or at least did, before Scott Brown was elected.
As hard-working Americans struggle through one of the worst recessions in U.S. history, one part of the country remains recession-proof: Washington, D.C.
Even though federal tax revenues are down 20 percent and the national debt has ballooned to $12 trillion, President Barack Obama and his allies on Capitol Hill continue to believe that we can borrow and spend our way to prosperity. As part of that plan, they're using our hard-earned tax dollars to increase the size of government and the salary of bureaucrats.
While the private sector has lost a total of 7.7 million jobs during the past two years, the ranks of the federal bureaucracy have swelled by nearly 10 percent. Furthermore, while the average salary in the private sector is $40,331, a typical federal worker earns $71,206. Worst of all is the explosion of government salaries at a time when most taxpayers are struggling to make ends meet.
Since the recession began in December 2007, the U.S. economy has been shedding jobs at its worst rate since the Great Depression. But you would never know it if you worked "inside the Beltway." When the economy turned south two years ago, the Department of Defense had 1,868 employees earning $150,000 or more. Today, there are 10,100 employees at the Pentagon taking home that salary. At the start of the economic slump, the Department of Transportation had only a single career employee earning more than $170,000. Today, there are more than 1,600 career federal workers at the DOT making that amount. Obama has recommended an additional 2 percent pay raise for 2010. That's unconscionable.
The time has come for Washington to live within its means. If most Americans are coping with a weak economy by tightening their belts, our public servants can to do the same. That's why I am calling for a salary freeze on all federal salaries above $120,000 until unemployment is under 7 percent, which should be in the next two or three years. Those who are earning three times as much as their peers in the private sector can make do until we reach that benchmark.
The only way we can rebuild our economy is to spur job growth in the private sector. It is the private sector – not government – that is the engine of our prosperity. After all, every single government job must be paid for through tax revenues – and those revenues come from the private sector. Increasing employment in the federal government is no solution at all. Indeed, by raising the price of government at a time when tax revenues are plunging at the fastest rate in 80 years, we are plunging our nation into its greatest debt crisis in history.
According to the president's own budget, we will add $9 trillion in government debt over the next decade, bringing the total national debt to $21 trillion. That doesn't even include the Democrats' health care bill which – if passed – will cost at least hundreds of billions more. That is the economic equivalent of medical malpractice, and it must stop.
If we freeze the pay of the highest-paid federal employees – including members of Congress – it won't eliminate our deficit overnight. But it will send a powerful message to the folks in Washington that they work for the taxpayers; not the other way around.
The bureaucrats might complain if the freeze drags on year after year. But my response is simple: If you want a raise, help the private sector start hiring people again. If you want more money, do something about unemployment.
This is an issue where conservatives will naturally take the lead, but we invite Democrats and independents to join us, as well. All Americans can rally around this common-sense issue which is about establishing fairness, accountability, and restoring fiscal sanity to the federal government.
The problem is that, over the last 40 years (or so), the entire economic system has turned into a battle-of-the-scams.
Like it or not, the entire country now realizes that if you're not running a scam on somebody (or participating in one) you're not going to make money.
Socialism (applied real-world socialism, not fantasy socialism) IS completely ONLY absolutely about using political influence to scam somebody. The system is working perfectly IF you happen to be in on a scam. Stop bitching, and find a good scam.
Federal workers earn 30-40% more than their private sector counterparts, qualify for a three-tier retirement plan which includes lifetime pensions, and may retire while still in their 50s, yet those who pay their salaries may have to wait until 70 to collect reduced Social Security benefits. Federal workers and contractors produce nothing and add nothing to the GDP; virtually all they do is rule over and regulate every aspect of our lives.
More than 77,000 federal workers earned more than the governors of their states in 2009, according to a new report.
The research found 18,351 federal medical officers earned more than their governors -- the most common occupation to out-earn states' top government executives. More than 5,000 air traffic controllers, 4,346 attorneys, 16 outdoor recreation planners and one interior designer also earned more than the governors of their respective states, the report said.
The Congressional Research Service report, requested by Sen. Tom Coburn, R-Okla., based its comparison on 2009 federal salary data from the Office of Personnel Management and 2009 salaries of governors from the Council of State Governments. The research is dated May 6 and was first reported Tuesday by The Washington Times.
The report did not examine salaries of employees in the Office of the Vice President, White House, CIA, U.S. Postal Service or a handful of other government agencies.
Governor salaries ranged between $70,000 in Maine and $212,179 in California in 2009, according to the report, which noted that California Republican Gov. Arnold Schwarzenegger waived his payment while in office. The governors of Virginia and New Jersey tied for fifth highest salaries in 2009 at $175,000; in Virginia, 606 feds earned more than that figure.
Colorado had the most federal employees -- 10,875 -- with salaries higher than the state's governor, who earned $90,000 in 2009. Maryland placed second, with 7,283 feds earning more than Democratic Gov. Martin O'Malley's salary of $150,000 -- including 2,266 medical officers, 51 employees in human resources, and 30 employees in information and arts. Delaware had the fewest number of federal employees -- 37 -- earning more than the governor, the report found.
The American Federation of Government Employees, the largest federal employee union, pointed to proposed legislation that would cap at $200,000 federal reimbursement for contractor salaries.
"The government's paying $700,000 and more for contractor salaries, and Sen. Coburn worries about the pay of physicians who care for wounded soldiers?" Beth Moten, AFGE's legislative and political director, asked in an emailed statement.
In an emailed response to Government Executive, Coburn said no one would disagree that federal employees should be paid adequately.
"We can all agree on the importance of paying highly specialized doctors to care for wounded soldiers and veterans, or skilled engineers for their services," he said. "However, when our nation is over $14 trillion in debt and American families are struggling to make ends meet, this report begs for an explanation of why interior designers, recreation planners and other public employees are enjoying higher salaries than state governors."
The highest paid federal employees in 2011 worked primarily in the medical field at government health agencies, according to data compiled by a company that specializes in connecting businesses through technology.
The top 1,000 federal salaries this year ranged from $216,345 to $350,000, with most of the highest earners working at the National Institutes of Health and at the Indian Health Service, according to the data. WikiOrgCharts, a company that seeks to connect businesses and people through a social customer relationship management tool, requested the information from the government through the Freedom of Information Act and developed a crowdsourced database that contains profiles of 1.2 million federal employees. The profiles list employees' names, title or job field, agency, and in many cases, their annual base salary.
"Some people can look at this and say these public servants make too much money," said Farhan Memon, WikiOrgCharts founder and chief executive officer. But Memon said many of the top earners are having a "generational impact" on the study of disease and could command much more in the private sector. "I don't know that you can put a price tag on that," he said.
Topping the 2011 list is Dr. Electron Kebebew, a medical officer at NIH who is widely regarded in the field of cancer research. Dr. Anthony Fauci, who directs the National Institute of Allergy and Infectious Diseases, garnered the No. 3 slot on the list, earning an annual salary of $335,000 in 2011. Fauci has led NIAID since 1984 and is one of the country's leading clinicians and researchers in the field of HIV/AIDS.
Other top earners included employees at the Farm Credit Administration, Federal Deposit Insurance Corporation, and the Securities and Exchange Commission.
Memon said some people have contacted WikiOrgCharts requesting removal from the database, which anyone can access. But the information contained in it is public and most government employees on the list understand that, he said, adding that centralizing such data and making it easy to search improves government transparency. In addition, the database serves as a kind of LinkedIn or similar social media tool, helping people in and out of government connect with one another. For example, Memon said one government contractor used the database to figure out the appropriate federal contact, while another used the information as a recruiting tool to see how much a potential hire was earning.
WikiOrgCharts also created organizational charts with employee profiles for certain large private sector companies, including Wal-Mart, Exxon-Mobil, Apple and Google.
Memon said he expects WikiOrgCharts will produce more lists and compilations based on the government data.
"Once you have a data set, there are multiple ways to cut and slice it," he said.
The 2012 Defense authorization bill, which the Senate passed Thursday night in a 93-7 vote, includes an amendment to cap the amount that defense contractors can be reimbursed for any employee's salary at $400,000.
Such a cap is opposed by many in the contractor community, and the Obama administration has favored a lower cap that would apply only to senior executives.
The amendment, approved by voice vote, was offered by Sens. Barbara Boxer, D-Calif.; Chuck Grassley, R-Iowa; and Jay Rockefeller, D-W.Va.
Under current law, a contractor can charge taxpayers $693,951 for the salaries of each of its five highest-paid employees, based on a formula adopted in the late 1990s.
"Taxpayers should not be on the hook for exorbitant government contractor salaries," Boxer said in a statement. "This amendment ensures that no defense contractor will make more in taxpayer funds than the president of the United States."
"We can't afford to waste increasingly limited defense dollars. This amendment goes after an unnecessary expenditure by containing runaway spending in a type of contract used extensively by the Department of Defense."
The House-passed version of the Defense bill would extend the current cap of slightly less than $700,000 to all employees.
The Boxer amendment is opposed by an alliance of contractors called the Acquisition Reform Working Group. In a Nov. 29 letter, the group warned it "could force companies to reduce its employees' compensation; in turn, these shrinking salaries will make the defense sector less attractive to top talent, which could then negatively impact DoD missions."
The harm to defense companies from lowering the cap, the contractors continued, "would be further compounded by broadening the scope of application to cover all federal contractor employees; highly skilled innovators and technology experts would likely focus their skill sets on the commercial market, thus eliminating the government's ability to develop effective critical mission solutions."
Debate on the Senate floor was tinged by the week's broader political dispute over whether to raise taxes on the wealthy to pay for an extension of a "holiday" on Social Security taxes.
Majority Leader Harry Reid, D-Nev., said, "while targeting the middle class, Republicans proposed to do nothing to cut back on excessive subsidies for many large corporations that benefit from government contracts." Reid said the contractors, who now total 5 million, "caught fire during the Republican control of the presidency."
Minority Leader Mitch McConnell, R-Ky., said his party's proposal to pay for the Social Security holiday by extending the freeze on federal pay, "is a much smarter approach to extending the temporary payroll tax cut than the one proposed by Democrats involving permanent tax hikes on job creators."


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Lending a Helping Hand
Skid Row resident Suzette Shaw, right, speaks during the Homelessness in Los Angeles panel discussion at UCLA Luskin. Photo by George Foulsham
Lending a Helping Hand Panel discussion at UCLA Luskin highlights what is and isn't being done to serve the burgeoning homeless population in L.A. County
November 20, 2017 /0 Comments/in School of Public Affairs, The Lewis Center, Urban Planning Michael Lens /by George Foulsham
By Zev Hurwitz
With nearly 60,000 Angelenos struggling with homelessness, local change agents have taken on the task of developing policies and services to address the crisis.
At a Nov. 15, 2017, panel discussion at the UCLA Luskin School of Public Affairs, four leaders in the field discussed the challenges and opportunities in finding solutions for the plethora of Los Angeles residents who do not have access to permanent housing.
Michael Lens, associate professor of urban planning at the Luskin School, moderated the "Homelessness in Los Angeles" event. Other participants were Jerry Ramirez, manager of Los Angeles County's homeless initiative; Dora Leon Gallo, CEO of A Community of Friends; Jordan Vega, a current UCLA student and a director of Bruin Shelter, a registered student organization; and Skid Row resident Suzette Shaw.
Lens began the lunch program by noting some alarming homelessness statistics and emphasizing the importance of having the conversation.
"Many of us are familiar with the fact that homelessness is very much on the rise in Los Angeles County," he said. "In January of 2017, volunteers counted over 58,000 people experiencing homelessness across L.A. County, which is a 23 percent rise over the previous year."
Lens pointed out that 34,000 of those people are in the City of Los Angeles. Within the city, 25,000 homeless are living "unsheltered" and 11,000 fell into the category of "chronically homeless.
"These are large numbers historically, and they're large numbers for any city," he said.
Gallo's organization, A Community of Friends, works with the local government and other non-profits to provide permanent supportive housing for the homeless. The group, which launched nearly 30 years ago with a grant from the county's Department of Mental Health, manages 47 buildings and provides in-house services in 18 of those buildings.
Gallo said that her group believes in a "housing first" approach to homelessness and that the model for permanent housing relies on subsidies that enable tenants to pay a fraction of their income in rent, no matter how small that income, without sacrificing the community aspect of living in Los Angeles.
"There really was no housing provider out there that was providing housing that is affordable," she said. "Our initial founders wanted to create a community where people would have friends.
Dora Leon Gallo, CEO of A Community of Friends, speaks during the panel discussion. Photo by George Foulsham
Earlier this year, L.A. County voters approved Measure H — a tax expected to raise $355 million for homeless services over the next 10 years. The county has developed 21 strategies for addressing homelessness and plans to use Measure H funding to increase housing and services for the county's homeless. Separately, city voters in 2016 passed Proposition HHH — a bond measure that will directly fund new housing units for low-income and housing insecure Angelenos.
"The 1.2 billion (dollars) from Proposition HHH is for the construction of permanent supportive housing," Ramirez said. "Where Measure H comes in, it really complements supportive housing because it's millions of dollars to provide the services. Half the challenge is getting a home for a homeless person — then the hard work begins in keeping them there."
Ramirez said that the county is hoping to bring in more partners like A Community of Friends to help map out the landscape for new programs and housing units to be funded under Measure H.
"We're trying to be very inclusive in this process because the county can't do it alone," he said. "We're trying to be inclusive, collaborative and transparent."
Not all services are being provided at the regional level. Vega helps run Bruin Shelter, which launched last year and currently provides beds for six housing insecure UCLA students. It is the first student-run shelter for peers in the country.
Vega's personal experience with friends who struggled with homelessness inspired him to take on the role at Bruin Shelter, which helps operate the shelter of Students4Students. Students have access to UCLA medical and social welfare students who provide case management services.
"Our space is kind of small — we're next to a church," he said. "We're currently under construction, hoping to expand, so that we can accommodate more students."
Suzette Shaw is a resident of Skid Row and knows firsthand the struggles that homeless people can face living on the streets.
"We need to make sure that now that we have the dollars, we are intentionally allocating them and very proactive in allocating those funds to organizations and individuals who make sure that the dollars are addressing the needs of the people," she said.
Shaw used to run a business and commuted long distances to work to try to make ends meet before moving to Skid Row. She's now living in a housing unit under her Section Eight voucher, which she had for nine months before receiving a unit. Shaw is very open about her story because people need to have more exposure to homeless in order to address the crisis.
"People tend to stereotype and sensationalize what poverty looks like," Shaw said. "We have to get real about who we are. We talk about NIMBY-ism, 'not-in-my-backyard.' People are either going to live on the sidewalk next to you or else you're going to make a space for them in the building next to you."
The issue is one of basic human rights for Shaw.
"I may be poor and I may live on the brink, but I do deserve housing and housing should be a human right," she said.
The talk was part of an ongoing Housing, Equity and Community series put on by the UCLA Lewis Center, which co-sponsored the event with the Institute on Inequality and Democracy at UCLA Luskin and the UCLA Ziman Center for Real Estate. The Lewis Center plans to hold more events in the winter and spring quarters on housing issues.
Monkkonen Research Informs New Model for Affordable Housing
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