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\noindent Statistica Sinica {\bf 13}(2003), 495-506
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\centerline{\large\bf ON STEIN'S IDENTITY FOR POSTERIOR NORMALITY}
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\centerline{Ruby C. Weng}
\vspace{.4cm}
\centerline{\it National Chengchi University}
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\begin{quotation}
\noindent {\it Abstract:}
We propose a new method to derive posterior normality
of stochastic processes. For a suitable parameter
transformation $Z_t$,
the likelihood function is converted to a form
close to a standard normal density.
Then we apply a version of Stein's Identity to obtain
an expression for the posterior expectation. From this,
posterior normality of $Z_t$ can be established.
Applications of this method are illustrated by
the conditional exponential family and a
nonhomogeneous Poisson process. \par
\vspace{9pt}
\noindent {\it Key words and phrases:}
Maximum likelihood estimator, posterior distributions, posterior normality,
Stein's identity, stochastic processes.\par
\end{quotation}
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