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Title: A general Bayes theory of nested model comparisons
Author: Chadwick, Thomas Jonathan
ISNI:       0000 0001 3525 8798
Awarding Body: Newcastle University
Current Institution: University of Newcastle upon Tyne
Date of Award: 2002
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We propose a general Bayes analysis for nested model comparisons which does not suffer from Lindley's paradox. It does not use Bayes factors, but uses the posterior distribution of the likelihood ratio between the models evaluated at the true values of the nuisance parameters. This is obtained directly from the posterior distribution of the full model parameters. The analysis requires only conventional uninformative or flat priors, and prior odds on the models. The conclusions from the posterior distribution of the likelihood ratio are in general in conflict with Bayes factor conclusions, but are in agreement with frequentist likelihood ratio test conclusions. Bayes factor conclusions and those from the BIC are, even in simple cases, in conflict with conclusions from HPD intervals for the same parameters, and appear untenable in general. Examples of the new analysis are given, with comparisons to classical P-values and Bayes factors.
Supervisor: Not available Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Statistics