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Abstract:
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A large part of Bayesian data analysis is based on examining the posterior distributions of parameters. In comparing different models, however, parameters can change their interpretations, and it is helpful to have a more stable platform for comparison. One popular approach is to examine the posterior distribution of the likelihood, or to compare the likelihood as evaluated using different models. While the parameters of a model identify the structure, the likelihood corresponds to the ability of a model to explain the observed data. Many questions, such as ``how informative is a particular variable'' or ``what is the importance of an interaction'' are better answered in terms of a change in likelihood than in terms of parameter values. Our goal in this research is to understand any fitted complex model in terms of its simpler building blocks.
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