Model Selection and Accounting for Model Uncertainty in Graphical Models Using OCCAM's Window
Abstract
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 which averages the posterior distributions of the quantity of interest under each of the models, weighted by their posterior model probabilities. However, this has not been used in practice because computing the posterior model probabilities is hard and the number of models is very large. 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 by averaging over a much smaller set of models.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 22, 1991
- Accession Number
- ADA241408
Entities
People
- Adrian Raftery
- David Madigan
Organizations
- University of Washington