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\noindent Statistica Sinica {\bf 13}(2003), 625-639

\vspace{3pc} \normalsize
\centerline{\large\bf A NONITERATIVE SAMPLING METHOD FOR}
\vspace{2pt}
\centerline{\large\bf COMPUTING POSTERIORS IN THE STRUCTURE OF}
\vspace{2pt}
\centerline{\large\bf EM-TYPE ALGORITHMS}
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\author{Ming Tan$^*$, Guo-Liang Tian$^*$ and Kai Wang Ng$^{\dag}$}
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\centerline{\it $^*$University of Maryland at Baltimore and $^\dag$The
University of Hong Kong}
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\begin{quotation}
\noindent {\it Abstract:}
We propose a noniterative sampling approach by combining the {\it
inverse Bayes formulae} (IBF), sampling/importance resampling and posterior mode
estimates from the Expectation/Maximization (EM) algorithm to obtain an
i.i.d.~sample
approximately from the posterior distribution for problems where the EM-type
algorithms apply. The IBF shows that the posterior is proportional to the ratio of
two conditional distributions and its numerator provides a natural class of built-in
{\it importance sampling functions} (ISFs) directly from the model specification.
Given that the posterior mode by an EM-type algorithm is relatively easy to obtain,
a best ISF can be identified by using that posterior mode, which results in a large
overlap area under the target density and the ISF. We show why this procedure works
theoretically. Therefore, the proposed method provides a novel alternative to perfect
sampling and eliminates the convergence problems of Markov chain Monte Carlo methods.
We first illustrate the method with a proof-of-principle example and then apply the
method to hierarchical (or mixed-effects) models for longitudinal data. We conclude
with a discussion.\par
\vspace{9pt}
\noindent {\it Key words and phrases:}
Bayesian computation, data augmentation, EM algorithm,
Gibbs sampler, inverse Bayes formulae, MCMC, sampling/importance
resampling.\par
\end{quotation}
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