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\begin{center}
\LARGE{\bf BAYESREG OBJECT b: regression procedure}
\end{center} 
\vspace{1cm}

\noindent {\bf \large Response:}
\begin{tabbing}
Number of observations: \= 210\\
Response Variable: \> y\\
Family: \> Gaussian\\
\end{tabbing}

\noindent {\bf \large Predictor:}\\


\begin{tabular}{ccp{12cm}}
$\eta$ & $=$ & $\gamma_{const}const + f_{x}(x) + f_{id}(id)$
\end{tabular}
\\ 
\\

\noindent {\bf \large Priors:}\\
\\
Fixed effects:\\
diffuse priors\\
\\\\
$f_{x}(x)$:\\
P-spline with second order random walk penalty\\
Number of knots: 8\\
Knot choice: equidistant\\
Degree of Splines: 3\\
Inverse gamma prior for variance component with hyperparameters a=0.001 and b=0.001\\
\\\\
$f_{id}(id)$\\
Markov random field\\
Inverse gamma prior for variance component with hyperparameters a=0.001 and b=0.001\\
\\\\

\noindent {\bf \large MCMC Options:}
\begin{tabbing}
Levels for credible intervals: \= \\
Level 1: \> 95\\
Level 2: \> 80\\
Number of Iterations: \> 12000\\
Burn in: \> 2000\\
Thinning Parameter: \> 100
\end{tabbing}
\vspace{0.5cm}

 {\bf \large Estimation results for the deviance: }\\ 

{\bf Unstandardized deviance } 

\vspace{-0.4cm}
\begin{tabbing}
\hspace{3cm} \= \\
  Mean:           \> 693.80468 \\
  Std. Dev:       \> 14.925032 \\
  2.5\% Quantile:  \> 667.4179 \\
  10\% Quantile:  \> 675.55959 \\
  50\% Quantile:  \> 693.03026 \\
  90\% Quantile:  \> 714.72261 \\
  97.5\% Quantile:  \> 722.23004 \\
\end{tabbing}

{\bf Saturated deviance } 

\vspace{-0.4cm}
\begin{tabbing}
\hspace{3cm} \= \\
  Mean:           \> 211.75483 \\
  Std. Dev:       \> 20.28022 \\
  2.5\% Quantile:  \> 170.71869 \\
  10\% Quantile:  \> 186.76649 \\
  50\% Quantile:  \> 209.93272 \\
  90\% Quantile:  \> 239.57748 \\
  97.5\% Quantile:  \> 251.42836 \\
\end{tabbing}


 {\bf \large Estimation results for the DIC: }\\ 

{\bf DIC based on the unstandardized deviance } 

\vspace{-0.4cm}
\begin{tabbing}
\hspace{3cm} \= \\
deviance($\bar{\mu}$) \> 649.0103 \\
pD  \> 44.794386 \\
DIC  \> 738.59907 \\
\end{tabbing}

{\bf DIC based on the saturated deviance } 

\vspace{-0.4cm}
\begin{tabbing}
\hspace{3cm} \= \\
deviance($\bar{\mu}$) \> 165.51503 \\
pD \> 46.239802 \\
DIC \> 257.99464 \\
\end{tabbing}


 {\bf \large Estimation results for the scale parameter: }\\ 

\vspace{-0.4cm}
\begin{tabbing}
\hspace{3cm} \= \\
Mean  \> 1.59119 \\
Std. dev.:  \> 0.189236 \\
  2.5\% Quantile:  \>1.30414 \\
  10\% Quantile:  \>1.33929 \\
  50\% Quantile:  \>1.56993 \\
  90\% Quantile:  \>1.84688 \\
  97.5\% Quantile:  \>1.97113 \\
\end{tabbing}


\newpage 


\noindent {\bf \large Fixed Effects:}\\
\\
\begin{tabular}{|r|rrrrr|}
\hline
Variable & Mean & STD & 2.5\%-Quant. & Median & 97.5\%-Quant.\\
\hline
const & 1.65687 & 0.0876656 & 1.51333 & 1.65726 & 1.83511\\
\hline 
\end{tabular}

\newpage
\noindent {\bf \large Plots:}

\begin{figure}[h!]
\centering
\includegraphics[scale=0.6]{/home/nik/tmp1/exmodel_f_x_pspline}
\caption{Non--linear Effect of 'x'.
Shown are the posterior means together with 95\% and 80\% pointwise credible intervals.}
\end{figure}

\begin{figure}[h!]
\centering
\includegraphics[scale=0.6]{/home/nik/tmp1/exmodel_f_id_spatial_pmean}
\caption{Non--linear Effect of 'id'. Shown are the posterior means.}
\end{figure}

\begin{figure}[htb]
\centering
\includegraphics[scale=0.6]{/home/nik/tmp1/exmodel_f_id_spatial_pcat95}
\caption{Non--linear Effect of 'id'. Posterior probabilities for a nominal level of 95\%.
Black denotes regions with strictly negative credible intervals,
white denotes regions with strictly positive credible intervals.}
\end{figure}

\begin{figure}[htb]
\centering
\includegraphics[scale=0.6]{/home/nik/tmp1/exmodel_f_id_spatial_pcat80}
\caption{Non--linear Effect of 'id'. Posterior probabilities for a nominal level of 80\%.
Black denotes regions with strictly negative credible intervals,
white denotes regions with strictly positive credible intervals.}
\end{figure}
\end{document}
