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Bayesian analysis of outlier problems using divergence measures
Author(s) -
Peng Fengchun,
Dey Dipak K.
Publication year - 1995
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 - 10.2307/3315445
Subject(s) - gibbs sampling , mathematics , maximum a posteriori estimation , divergence (linguistics) , laplace's method , bayesian probability , outlier , posterior probability , a priori and a posteriori , combinatorics , statistics , maximum likelihood , philosophy , linguistics , epistemology
A Bayesian approach is presented for detecting influential observations using general divergence measures on the posterior distributions. A sampling‐based approach using a Gibbs or Metropolis‐within‐Gibbs method is used to compute the posterior divergence measures. Four specific measures are proposed, which convey the effects of a single observation or covariate on the posterior. The technique is applied to a generalized linear model with binary response data, an overdispersed model and a nonlinear model. An asymptotic approximation using Laplace method to obtain the posterior divergence is also briefly discussed.