Markov chain Monte Carlo model determination for hierarchical and graphical log-linear models

Δελλαπόρτας, Πέτρος

doi:10.1093/biomet/86.3.615

Cited by 130 publications

(191 citation statements)

References 29 publications

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“…Dellaportas & Forster, 1999), point out that even in this apparently small model selection exercise, one should look not only at the most probable graphs, as a considerable number of models may be quite alike in terms of support, but also at the posterior probabilities of edge presence.…”

Section: Discussion On Model Selectionmentioning

confidence: 99%

“…If the aim of the approximate inference is heavily focused on quantitative learning aspects we suggest considering, as a more powerful alternative, the reversible jump approach suggested in Giudici and Green (1999) and Dellaportas and Forster (1999) which does MCMC model determination over both the model and the parameter space.…”

Section: Discussionmentioning

confidence: 99%

“…We finally remark that alternative choices for the prior on the parameters are discussed, for example, in Dellaportas and Forster (1999). Furthermore, in order to alleviate possible sensitivity of the results to the prior hyperparameters, a hierarchical prior distribution may be considered, as in Giudici and Green (1999).…”

Section: Bayesian Graphical Model Scoringmentioning

confidence: 99%

“…Madigan et al (1996) extend the analysis considering model search over Markov equivalence classes of DAG models. Dellaportas and Forster (1999) consider a reversible jump MCMC algorithm over the broader class of hierarchical loglinear models.…”

Section: Coronary Heart Disease Datasetmentioning

confidence: 99%

“…We remark that, while MC 3 addresses the structural learning problem, the reversible jump algorithm, applied to graphical models in Giudici and Green (1999) and Dellaportas and Forster (1999), although certainly more difficult to implement and test, is indeed more suited for problems in which also quantitative learning requires the development of approximate inferences (as occurs, for instance, with incomplete data).…”

Section: Introductionmentioning

confidence: 99%

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2003

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Abstract. The motivation of this paper is the application of MCMC model scoring procedures to data mining problems, involving a large number of competing models and other relevant model choice aspects.To achieve this aim we analyze one of the most popular Markov Chain Monte Carlo methods for structural learning in graphical models, namely, the MC 3 algorithm proposed by D. Madigan and J. York (International Statistical Review, 63, 215-232, 1995). Our aim is to improve their algorithm to make it an effective and reliable tool in the field of data mining. In such context, typically highly dimensional in the number of variables, little can be known a priori and, therefore, a good model search algorithm is crucial.We present and describe in detail our implementation of the MC 3 algorithm, which provides an efficient general framework for computations with both Directed Acyclic Graphical (DAG) models and Undirected Decomposable Models (UDG). We believe that the possibility of commuting easily between the two classes of models constitutes an important asset in data mining, where an a priori knowledge of causal effects is usually difficult to establish.Furthermore, in order to improve the MC 3 method we propose provide several graphical monitors which can help extracting results and assessing the goodness of the Markov chain Monte Carlo approximation to the posterior distribution of interest.We apply our proposed methodology first to the well-known coronary heart disease dataset (D. Edwards & T. Havránek, Biometrika, 72:2, 339-351, 1985). We then introduce a novel data mining application which concerns market basket analysis.

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Section: Discussion On Model Selectionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Bayesian Graphical Model Scoringmentioning

confidence: 99%

Section: Coronary Heart Disease Datasetmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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2003

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B ayesian Methods for Contingency Tables

Albert

2005

Encyclopedia of Biostatistics

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Bayesian alternatives to frequentist methods for fundamental problems in categorical data analysis, such as testing independence in two‐way contingency tables and estimating probabilities of categories containing no observations, have been considered for at least four decades. Since the 1980s, Bayesian methods of model selection have also seen extensive and continuing development. These attempt to address the tendencies of frequentist approaches to arrive at overly complex models, and to disregard the effects of variability in model selection on model‐based estimated effects and predictions. This entry briefly reviews several Bayes and empirical Bayes approaches to estimating probabilities of categories, testing equiprobability in a one‐way table, testing independence in a two‐way contingency table, and selecting among generalized linear models, with particular attention to loglinear models, for tables of higher dimension.

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Bayesian Methods for Categorical Data

Gutiérrez‐Peña¹

2005

Encyclopedia of Statistics in Behavioral Science

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The Bayesian approach to statistical inference is based on a subjective interpretation of probability. Given a prior distribution describing our prior beliefs concerning the value of an unknown quantity, Bayes' theorem allows us to update those beliefs in the light of observed data. The resulting posterior distribution then summarizes all the available information about the quantity of interest, conditional on the posited model. Bayesian methods for the analysis of categorical data use the same classes of models as the classical approach. However, Bayesian analyses can be more informative – the posterior distribution of the parameter contains more information than mere point estimates or test statistics – and may provide more natural solutions in certain situations such as those involving sparse or missing data, or unidentifiable parameters.

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Markov chain Monte Carlo model determination for hierarchical and graphical log-linear models

Cited by 130 publications

References 29 publications

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B ayesian Methods for Contingency Tables

Bayesian Methods for Categorical Data

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