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Title: Posterior propriety for hierarchical models with log-likelihoods that have norm bounds

Statisticians often use improper priors to express ignorance or to provide good frequency properties, requiring that posterior propriety be verified. Our paper addresses generalized linear mixed models, GLMMs, when Level I parameters have Normal distributions, with many commonly-used hyperpriors. It provides easy-to-verify sufficient posterior propriety conditions based on dimensions, matrix ranks, and exponentiated norm bounds, ENBs, for the Level I likelihood. Since many familiar likelihoods have ENBs, which is often verifiable via log-concavity and MLE finiteness, our novel use of ENBs permits unification of posterior propriety results and posterior MGF/moment results for many useful Level I distributions, including those commonly used with multilevel generalized linear models, e.g., GLMMs and hierarchical generalized linear models, HGLMs. Furthermore, those who need to verify existence of posterior distributions or of posterior MGFs/moments for a multilevel generalized linear model given a proper or improper multivariate F prior as in Section 1 should find the required results in Sections 1 and 2 and Theorem 3 (GLMMs), Theorem 4 (HGLMs), or Theorem 5 (posterior MGFs/moments).
 [1] ;  [2]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. Harvard Univ., Cambridge, MA (United States)
Publication Date:
Report Number(s):
Journal ID: ISSN 1931-6690
Grant/Contract Number:
Accepted Manuscript
Journal Name:
Bayesian Analysis
Additional Journal Information:
Journal Volume: 10; Journal ID: ISSN 1931-6690
Research Org:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org:
Country of Publication:
United States
97 MATHEMATICS AND COMPUTING; exponentiated norm bound; generalized linear mixed model; hierarchical generalized linear model; improper prior; multilevel objective Bayes
OSTI Identifier: