Name: POSTERIOR PREDICTIVE ASSESSMENT OF MODEL FITNESS VIA REALIZED DISCREPANCIES
Authors: Andrew Gelman, Xiao-Li Meng and Hal Stern
Statistica Sinica 6 (1996), 733-807
abstract: This paper considers Bayesian counterparts of the classical tests for goodness
of fit and their use in judging the fit of a single Bayesian model to the observed
data. We focus on posterior predictive assessment, in a framework that also includes
conditioning on auxiliary statistics. The Bayesian formulation facilitates the construction
and calculation of a meaningful reference distribution not only for any
(classical) statistic, but also for any parameter-dependent “statistic” or discrepancy.
The latter allows us to propose the realized discrepancy assessment of model
fitness, which directly measures the true discrepancy between data and the posited
model, for any aspect of the model which we want to explore. The computation
required for the realized discrepancy assessment is a straightforward byproduct of
the posterior simulation used for the original Bayesian analysis.