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Cited by 1,205Bayesian Modeling and Causal InferenceStatistical Methods and InferenceStatistical Methods and Bayesian Inference

The DOI matches its Crossref record; 53 of the 54 references it cites were found in a registry or an index.

Model Selection and Accounting for Model Uncertainty in Graphical Models Using Occam's Window

Madigan, David, Raftery, Adrian E.·1994·Journal of the American Statistical Association
DOI 10.1080/01621459.1994.10476894
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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 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 1011). 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 decomposable log-linear models, this is based on properties of chordal graphs and hyper-Markov prior distributions and the resultant calculations can be carried out locally. The end product is an overall strategy for model selection and accounting for model uncertainty that searches efficiently through the very large classes of models involved. Three examples are given. The first two concern data sets that have been analyzed by several authors in the context of model selection. The third addresses a urological diagnostic problem. In each example, our model averaging approach provides better out-of-sample predictive performance than any single model that might reasonably have been selected.

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Citations

Cites

Show all 54 references

Research works printed but not linked: 12

  1. 10.1007/BF00994110 · DOI
  2. Edwards D., 1990, Journal of the Royal Statistical Society, 52, 3
  3. Evett I. W., paper presented to the Fourth Valencia International Meeting on Bayesian Statistics
  4. Jeffreys H., 1961, Theory of Probability,
  5. Kotz , S. and Johnson , N. L. , eds. 1985.Encyclopedia of Statistical Sciences, Vol. 6, 578–579. New York: John Wiley.
  6. 10.2307/2981576 · DOI
  7. Pearl J., Knowledge Representation and Reasoning: Proceedings of the Second International Conference, 441
  8. Raftery A. E., 1988, “Approximate Bayes Factors for Generalized Linear Models,”
  9. Raftery A. E., 1993, “Approximate Bayes Factors and Accounting for Model Uncertainty in Generalized Linear Models,”
  10. Sakamoto, 1984, Metron, 40, 257
  11. Spiegelhalter D. J., 1982, Journal of the Royal Statistical Society, 44, 377
  12. Whittaker J., 1984, Compstat 84, 401

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Metadata

Authors
Madigan, D., & Raftery, A. E.
Affiliations
University of Washington (US)
ORCID
Venue
Journal of the American Statistical Association
Publisher
Informa UK Limited
Published
1994-12
Volume
89
Issue
428
Pages
1535-1546
ISSN
  • 0162-1459 (ISSN-L)
  • 1537-274X
DOI
10.1080/01621459.1994.10476894
OpenAlex
W2111051773
Cited by
1,205
References
54
Citations by year
2026: 18 · 2025: 17 · 2024: 34 · 2023: 28 · 2022: 32 · 2021: 48 · 2020: 48 · 2019: 60 · 2018: 78 · 2017: 39 · 2016: 35 · 2015: 44 · 2014: 55 · 2013: 50 · 2012: 62
FWCI
35.01
Type
journal article
Language
en
Open access
closed
Locations
  • Journal of the American Statistical Association (publishedVersion)
  • Defense Technical Information Center (DTIC) (submittedVersion)
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Modeling and Causal Inference
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
Keywords
model selection, model uncertainty, Bayesian model averaging, posterior model probabilities, Bayes factor, chordal graphs, expert systems, out-of-sample forecasting, urological diagnosis

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