Abstract
We consider the problem of model selection for Bayesian graphical models, and embed it in the larger context of accounting for model uncertainty. Data analysts typically select a single model from some class of models, and then condition all subsequent inference on this model. However, this approach ignores model uncertainty, leading to poorly calibrated predictions: it will often be seen in retrospect that one’s uncertainty bands were not wide enough. The Bayesian analyst solves this problem by averaging over all plausible models when making inferences about quantities of interest. In many applications, however, because of the size of the model space and awkward integrals, this averaging will not be a practical proposition, and approximations are required. Here we examine the predictive performance of two recently proposed model averaging schemes. In the examples considered, both schemes outperform any single model that might reasonably have been selected.
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Bradshaw, J.M., Chapman, C.R., Sullivan, K.M., Boose, J.H., Almond, R.G., Madigan, D., Zarley, D., Gavrin, J., Nims, J. and Bush, N. (1993) “KS-3000: An application of DDUCKS to bone- marrow transplant patient support”, Proc. 7th European Knowledge Acquisition for Knowledge- Based Systems Workshop (EKAW-93), Toulouse and Caylus, France, 57–74 A.
Breslow, N. (1991) “Biostatistics and Bayes”, Stat. Sci. 5, 269–298.
Draper, D., (1994) “Assessment and propagation of model uncertainty,” JRSS (B), to appear.
[41 Edwards, D. and Havránek, T. (1985) “A fast procedure for model search in multidimensional contingency tables”, Biometrika 72, 339–351.
Fowlkes, E.B., Freeny, A.E. and Landwehr, J.M. (1988) “Evaluating logistic models for large contingency tables”, JASA 83, 611–622.
Hastings, W.K. (1970) “Monte Carlo sampling methods using Markov chains and their applications”, Biometrika 57, 97–109.
Hodges, J.S. (1987) “Uncertainty, policy analysis and statistics”, Stat. Sci. 2, 259–291.
Kass, R.E. and Raftery, A.E. (1993) “Bayes factors and model uncertainty”. Technical Report 254, Department of Statistics, University of Washington.
Madigan, D. and Raftery, A.E. (1991) “Model selection and accounting for model uncertainty in graphical models using Occam’s window”. Technical Report 213, Department of Statistics, University of Washington.
Madigan, D. and York, J. (1993) “Bayesian graphical models for discrete data”. Technical Report 259, Department of Statistics, University of Washington.
Raftery, A.E. (1988) “Approximate Bayes factors for generalised linear models”. Technical Report 121, Department of Statistics, University of Washington.
Raftery, A.E. (1993) “Approximate Bayes factors and accounting for model uncertainty in generalised linear models”. Technical Report 255, Department of Statistics, University of Washington.
Regal, R. and Hook, E. (1991) “The effects of model selection on confidence intervals for the size of a closed population”, Stat. Med. 10,717–721.
Self, M. and Cheeseman, R (1987) “Bayesian prediction for artificial intelligence”, Proc. 3rd Workshop on Uncertainty in Artificial Intelligence, Seattle, 61–69
Tierney, L. (1991) “Markov chains for exploring posterior distributions”. Technical Report 560, School of Statistics, University of Minnesota.
Upton, G.J.G. (1991) “The exploratory analysis of survey data using log-linear models”, The Statistician 40,169–182.
Whittaker, J. (1990) Graphical models in Applied Mathematical Multivariate Statistics. John Wiley & Sons, Chichester, England.
York, J.C. and Madigan, D. (1992) “Bayesian methods for estimating the size of a closed population”, Technical Report 234, Department of Statistics, University of Washington.
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© 1994 Springer-Verlag New York
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Madigan, D., Raftery, A.E., York, J.C., Bradshaw, J.M., Almond, R.G. (1994). Strategies for Graphical Model Selection. In: Cheeseman, P., Oldford, R.W. (eds) Selecting Models from Data. Lecture Notes in Statistics, vol 89. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2660-4_10
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DOI: https://doi.org/10.1007/978-1-4612-2660-4_10
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