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Model selection and accounting for model uncertainty in graphical models using Occam's window
, 1993
"... We consider the problem of model selection and accounting for model uncertainty in highdimensional contingency tables, motivated by expert system applications. The approach most used currently is a stepwise strategy guided by tests based on approximate asymptotic Pvalues leading to the selection o ..."
Abstract

Cited by 365 (48 self)
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We consider the problem of model selection and accounting for model uncertainty in highdimensional contingency tables, motivated by expert system applications. The approach most used currently is a stepwise strategy guided by tests based on approximate asymptotic Pvalues 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 which 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 maximising predictive ability. However, 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 1011). We argue that the standard Bayesian formalism is unsatisfactory and we propose an alternative Bayesian approach that, we contend, takes full account of the true model uncertainty byaveraging overamuch smaller set of models. An efficient search algorithm is developed for nding these models. We consider two classes of graphical models that arise in expert systems: the recursive causal models and the decomposable
MODEL SELECTION AND SIMPLIFICATION USING LATTICES
"... This paper shows how to cope with a problem of model selection and simplication using the principle of coherence (Gabriel (1969): Aprocedure involving testing a set of models ought not accept a model while rejecting a more general model). The mathematical lattice theory is used to de ne a partial or ..."
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This paper shows how to cope with a problem of model selection and simplication using the principle of coherence (Gabriel (1969): Aprocedure involving testing a set of models ought not accept a model while rejecting a more general model). The mathematical lattice theory is used to de ne a partial ordering over the space of considered models. Several examples of partial ordering in large families of models are given along with a searching algorithm to determine the best model with respect to chosen criteria.