Bayesian asymptotics under misspecification
Year: 2004
Type: dissertation
Abstract: We prove that the posterior distribution based on an i.i.d. sample in misspecified parametric models converges to a normal limit in total variation under conditions that are comparable to those in the well-specified situation. Besides regularity conditions, uniform testability against fixed alternatives and sufficiency of prior mass in neighbourhoods of the point of convergence are required. The rate of convergence is considered in detail, with special attention for the existence and construction of suitable test sequences. We also give a lemma to exclude testable model subsets which implies a misspecified version of Schwartz’ consistency theorem, establishing weak convergence of the posterior to a measure degenerate at the point at minimal Kullback-Leibler divergence with respect to the true distribution.
Author: B. J. K. Kleijn
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1556833046