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On Bayesian consistency
Author(s) -
Walker Stephen,
Hjort Nils Lid
Publication year - 2001
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00314
Subject(s) - hellinger distance , consistency (knowledge bases) , sequence (biology) , bayesian probability , exponential family , posterior probability , simple (philosophy) , mathematics , posterior predictive distribution , prior probability , exponential distribution , statistical physics , statistics , bayesian linear regression , bayesian inference , discrete mathematics , physics , philosophy , genetics , epistemology , biology
We consider a sequence of posterior distributions based on a data‐dependent prior (which we shall refer to as a pseudoposterior distribution) and establish simple conditions under which the sequence is Hellinger consistent. It is shown how investigations into these pseudo posteriors assist with the understanding of some true posterior distributions, including Pólya trees, the infinite dimensional exponential family and mixture models.