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

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
Open this paper in CoChat — free account

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.

Integrity signals

Registry

Crossref · 10.1080/01621459.1994.10476894

Cites

53 of 53 references verified0 citation errors · 0 not checkable

Statistics

Recomputing p-values needs the paper’s full text.

Claims the paper makes

This paper’s full text isn’t openly available, so its claims and self-check weren’t run. The registry and citation checks still apply.

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • The number of models in Occam's window is a useful indicator of how peaked the posterior is, with smaller values corresponding to peakier posteriors.

    “The number of models in the window, , is a useful indicator as smaller values correspond to peakier posteriors.”

    From Comparing families of dynamic causal models (2010) · cites this paper as [38]

Cites

Flagged first, then by citations

1 of the 54 references couldn’t be matched to a known paper.

Cited by

Sorted by citations

Related

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

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review