Premium
A Graphical Diagnostic for Identifying Influential Model Choices in Bayesian Hierarchical Models
Author(s) -
SCHEEL IDA,
GREEN PETER J.,
ROUGIER JONATHAN C.
Publication year - 2011
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2010.00717.x
Subject(s) - posterior probability , graphical model , mathematics , bayesian probability , bayesian hierarchical modeling , econometrics , graph , hierarchical database model , plot (graphics) , prior probability , statistical model , conditional probability distribution , statistics , bayesian inference , computer science , data mining , combinatorics
. Real‐world phenomena are frequently modelled by Bayesian hierarchical models. The building‐blocks in such models are the distribution of each variable conditional on parent and/or neighbour variables in the graph. The specifications of centre and spread of these conditional distributions may be well motivated, whereas the tail specifications are often left to convenience. However, the posterior distribution of a parameter may depend strongly on such arbitrary tail specifications. This is not easily detected in complex models. In this article, we propose a graphical diagnostic, the Local critique plot , which detects such influential statistical modelling choices at the node level. It identifies the properties of the information coming from the parents and neighbours (the local prior) and from the children and co‐parents (the lifted likelihood) that are influential on the posterior distribution, and examines local conflict between these distinct information sources. The Local critique plot can be derived for all parameters in a chain graph model.