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\footnotesize \noindent Statistica Sinica {\bf 21} (2011), 1687-1711

\footnotesize \noindent doi:http://dx.doi.org/10.5705/ss.2009.282

\vspace{3pc} \normalsize \centerline{\large\bf CONVERGENCE OF THE
EQUI-ENERGY SAMPLER} \vspace{2pt} \centerline{\large\bf  AND ITS
APPLICATION TO THE ISING MODEL} \vspace{.25cm}
\author{Xia Hua and S. C. Kou}
\vspace{.4cm} \centerline{\it Massachusetts Institute of Technology
and Harvard University} \vspace{.55cm} 
\begin{quotation}
\noindent {\it Abstract:} We provide a complete
 proof of the
convergence of a recently developed sampling algorithm called the
equi-energy (EE) sampler (\cite{Kou}) %, Zhou, and Wong (2006))
 in
the case that the state space is countable. In a countable state
space, each sampling chain in the EE\ sampler is strongly ergodic
a.s.~with the desired steady-state distribution. Furthermore, all
chains satisfy the individual ergodic property. We apply the EE
sampler to the Ising model to test its efficiency, comparing it with
the Metropolis algorithm and the parallel tempering algorithm. We
observe that the dynamic exponent of the EE sampler is significantly
smaller than those of parallel tempering and the Metropolis
algorithm, demonstrating its high efficiency.\par \vspace{9pt}
\noindent {\it Key words and phrases:} Dynamic exponent, ergodic
property, Monte Carlo methods, phase transition, steady-state
distribution, temperature, transition kernel. \par
\end{quotation}

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