Model Selection and Accounting for Model Uncertainly in Graphical Models Using Occam's Window
Journal article by David Madigan, Adrian E. Raftery; Journal of the American Statistical Association, Vol. 89, 1994
Journal Article Excerpt
Model Selection and Accounting for Model Uncertainly in Graphical Models Using Occam's Window. by DAVID MADIGAN , ADRIAN E. RAFTERY ADRIAN E. RAFTERY [*] We consider the problem of model selection and accounting for model uncertainty in high-dimensional contingency tables, motivated by expert system applications. The approach most used currently is a stepwise strategy guided by tests based on approximate asymptotic P values leading to the selection of a single model; inference is then conditional on the selected model. The sampling properties of such a strategy are complex, and the failure to take account of model uncertainty leads to underestimation of uncertainty about quantities of interest. In principle, a panacea is provided by the standard Bayesian formalism that averages the posterior distributions of the quantity of interest under each of the models, weighted by their posterior model probabilities. Furthermore, this approach is optimal in the sense of maximizing predictive ability. But this has not been used in practice, because computing the posterior model probabilities is hard and the number of models is very large (often greater than [10.sup.11]). We argue that the standard Bayesian formalism is unsatisfactory and propose an alternative Bayesian approach that, we contend, takes full account of the true model uncertainty by averaging over a much smaller set of models. An efficient search algorithm is developed for finding these models. We consider two classes of graphical models that arise in expert systems: the recursive causal models and the decomposable log-linear models. For each of these, we develop efficient ways of computing exact Bayes factors and hence posterior model probabilities. For the deco... |
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