Easy estimation of normalizing constants and Bayes factors by posterior
simulation: Stabilizing the harmonic mean estimator.
Easy estimation of normalizing constants and Bayes factors by posterior
simulation: Stabilizing the harmonic mean estimator.
J.M. Satagopan,
M.A. Newton , and A.E. Raftery.
Technical Report 1028, Department of Statistics,
University of Wisconsin, Madison.
First issued November 2000. Under review at JRSSb.
(Issued simultaneously as
TR 382 by the Department of Statistics, UW Seattle.)
Abstract:
The Bayes factor is a useful summary for model selection. Calculation
of this measure involves evaluating the integrated likelihood
(or prior predictive density), which can be estimated from the
output of MCMC and other posterior simulation methods using the
harmonic mean estimator. While this is a
simulation-consistent estimator, it can have infinite variance. In this
article we describe a method to stabilize the harmonic mean estimator.
Under this approach the parameter space is reduced such that the modified
estimator involves the harmonic mean of heavier tailed densities, thus
resulting in a finite variance estimator. We discuss general conditions
under which this reduction is applicable and illustrate the proposed
method through several examples.
Postscript
copy
NBA Data from which free throw example arises,
and some SPlus code to read it.