>\documentstyle[farsi,fmultico,ffancyhe]{article} >\textheight=22cm >\input{amssym} >\textwidth=16cm >\oddsidemargin=-1cm >\topmargin=1cm >\setlength{\columnsep}{0.7cm}% >\setlength{\evensidemargin}{-1cm} >\lhead[\fancyplain{}{\footnotesize\siah\thepage}]{\fancyplain{}{\footnotesize\siah\rightmark}} >\rhead[\fancyplain{}{\footnotesize\siah\leftmark}]{\fancyplain{}{\footnotesize\siah\thepage}} >\cfoot{} >\headrulewidth 1.5pt >\newcommand{\btheta}{\mbox{\boldmath{$\theta$}}} >\parindent=0cm \newtheorem{definition}{\noindent\bf\large\hspace*{-.4cm}ڗ} >\newtheorem{theorem}{\noindent\bf\large\hspace*{-.4cm}} >\newtheorem{lemma}{\noindent\bf\large\hspace*{-.4cm}} >\newtheorem{example}{\noindent\large\hspace*{-.4cm}} >\newtheorem{remark}{\noindent\large\hspace*{-.4cm}} >\newtheorem{proposition}{\noindent\large\hspace*{-.4cm}𥐤} < >\begin{document} >\baselineskip=0.8cm >\newcommand{\ds}{\displaystyle} >\newcommand{\eps}{\varepsilon} >\pagestyle{fancy} \setcounter{footnote}{0} >\setcounter{section}{0} >\setcounter{equation}{0} >\setcounter{definition}{0} >\setcounter{theorem}{0} >\setcounter{lemma}{0} >\setcounter{example}{0} >\setcounter{remark}{0} >\setcounter{proposition}{0} < \setlength{\unitlength}{1cm} >\begin{center} >%\unitlegth{1cm} >\begin{picture}(5.5,1.5) >\put(6,1){\special{em:graph 1.bmp}} >\end{picture}\\ >%\end{center} >%\vspace{.7cm} >%\begin{center} >\vspace{2.4cm} >\mbox{\small \siah >\siah\smallڐڨڗڪ} >\end{center} >\vspace{.5cm} < < < <ڐڛڨړڝڨڨڨ \setlength{\unitlength}{1cm} >\begin{center} >%\unitlegth{1cm} >\begin{picture}(8,4.5) >\put(12,5.5){\special{em:graph 2.bmp}} >\end{picture}\\ >%\end{center} >\vspace{2.1cm} >%\begin{center} >\vspace{2.4cm} >\mbox{\small \siah >\siah\smallړڪڨڐڨڗڪ} >\end{center} >\vspace{.5cm} < \begin{eqnarray} >E^\pi [g_k(\theta)]=\omega_k,~~~~k=1,...,K >\end{eqnarray} <$\theta$ڗ𨨗ړڗڛڐ$\pi$ڐڍړڬڥڗ >\begin{eqnarray*} >\varepsilon(\pi)=-\sum_{i=1}^\infty \pi(\theta_i)\log(\pi(\theta_i)) >\end{eqnarray*} <ڐڗڕڍڤړڢړڢڤھڬړڬڥړڢӆ >\begin{eqnarray*} >\pi^*(\theta_i)={{\exp\{\sum_{k=1}^K\lambda_k g_k(\theta_i)\}}\over{\sum_{j=1}^\infty >\exp\{\sum_{k=1}^K\lambda_k g_k(\theta_j)\}}} >\end{eqnarray*} <䢐$\lambda_k$ڮړڪړڤڢڤھ <$\theta$ڕړڗڝڐ$\pi$ڐړڗڍړڗڐ <$\pi_0$ڢړڢڐڐڍړڬڥڗӆ >\begin{eqnarray} >\varepsilon(\pi)&=&E^{\pi_0}[\log({{\pi(\theta)}\over{\pi(\theta_0)}})] \\ >\nonumber &=& \int\log({{\pi(\theta)}\over{\pi(\theta_0)}})~\pi_0(d\theta) >\end{eqnarray} <ڐڗڗڍڢڤھڬړڬڥړڢӆ >\begin{eqnarray} >\pi^*(\theta)={{\exp\{\sum_{k=1}^K\lambda_k g_k(\theta)\}\pi_0(\theta)}\over{\int >\exp\{\sum_{k=1}^K\lambda_k g_k(\eta)\}\pi_0(d\eta)}}. >\end{eqnarray}\vspace{-.5cm} < \begin{eqnarray*} >r(\pi,\delta)&=& E^\pi [R(\theta,\delta)] \\ >&=& \int_\Theta \int_\chi L(\theta, \delta(x))f(x|\theta)dx ~\pi(\theta)d\theta >\end{eqnarray*} \begin{eqnarray*} >\pi^*(\theta)\propto \exp\{\lambda\theta\} >\end{eqnarray*} <ڐڗڤړڬڗڐڢڬڐڐڐ$var(\theta)=\sigma^2$ <ڢړڕڍړڬڥړڢ >\begin{eqnarray*} >\pi^*(\theta)\propto \exp\{\lambda_1\theta+\lambda_2\theta^2\} >\end{eqnarray*} <ړڬڗ${\cal{N}}(-{\lambda_1\over{2\lambda_2}},-{1\over{2\lambda_2}})$ڮڢڍړڬڥ <ڢ >\begin{eqnarray*} >-{\lambda_1\over{2\lambda_2}}=\mu~~,~~-{1\over{2\lambda_2}}=\sigma^2 >\end{eqnarray*} <ړ >\begin{eqnarray*} >\lambda_1={\mu\over\sigma^2}~~,~~\lambda_2=-{1\over {2\sigma^2}}. >\end{eqnarray*} \english > \bibitem{3}~ Casella, G. and Berger, R.L. (2001), {\em Statistical Inference}, 2nd Ed., Duxbury Press, 35-40. > \bibitem{4}~ Green, P.J. (1995), Reversible jump Markov chain Monte Carlo computation and Bayesian model determination, >{\em Biometrika}, 82, 711-731. > \bibitem{5}~ Koski, T. (2005). Baysian statistics and MCMC computation (simulated annealing and optimization), >{\em www.mai.liu.se/ $\sim$ tikos/kurser/simulametrop3.pdf.} > \bibitem{6}~ Robert, C.P. and Casella, G. (1999). {\em Monte Carlo Statistical Methods}, 2nd Ed., Springer, Berlin.