A new general approach to Bayesian model comparisons
by Murray Aitkin
Abstract: This talk gives a brief statement of the general approach through posterior likelihoods, set out in detail in my 2010 book Statistical Inference: an Integrated Bayesian/Likelihood Approach (Chapman and Hall/CRC Press).
The idea is illustrated by a very simple example of a court case involving a possibly increased risk of encephalitis following MMR vaccination.
A complex example of mixture modelling of the recession velocities of galaxies illustrates the idea of stochastic ordering of likelihood or deviance distributions, and resolves the confusing inconsistencies of previous Bayesian analyses.
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