Statistica Sinica 13(2003), 495-506
ON STEIN'S IDENTITY FOR POSTERIOR NORMALITY
Ruby C. Weng
National Chengchi University
Abstract:
We propose a new method to derive posterior normality
of stochastic processes. For a suitable parameter
transformation 
,
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 can be established.
Applications of this method are illustrated by
the conditional exponential family and a
nonhomogeneous Poisson process.
Key words and phrases:
Maximum likelihood estimator, posterior distributions, posterior normality,
Stein's identity, stochastic processes.