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Model influence functions based on mixtures
Author(s) -
Gustafson Paul
Publication year - 1996
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315332
Subject(s) - bayes factor , a priori and a posteriori , bayes' theorem , posterior probability , prior probability , bayesian probability , parametric statistics , inference , bayesian inference , mathematics , perturbation (astronomy) , baseline (sea) , mixing (physics) , maximum a posteriori estimation , probability density function , statistical physics , statistics , computer science , physics , maximum likelihood , artificial intelligence , philosophy , oceanography , epistemology , quantum mechanics , geology
Influence functions are considered as diagnostics for model departures in parametric Bayesian inference. A baseline model density is expressed as a mixture; then the mixing distribution is perturbed. This is designed to engender perturbations which are plausible a priori. The influence of perturbations is measured for both Bayes estimates and their associated posterior expected losses. To assess the plausibility of perturbations a posteriori , an additional influence function is constructed for the Bayes factor comparing the perturbed and baseline models. The effect of perturbation on various estimands is incorporated in the analysis.