## Model Selection and Accounting for Model Uncertainty in Graphical Modsels using Occam's Window (1991)

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Venue: | JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION |

Citations: | 265 - 46 self |

### BibTeX

@ARTICLE{Madigan91modelselection,

author = {David Madigan and Adrian E. Raftery},

title = {Model Selection and Accounting for Model Uncertainty in Graphical Modsels using Occam's Window},

journal = {JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION},

year = {1991},

volume = {89},

pages = {1535--1546}

}

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### 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.