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The practical implementation of Bayesian model selection
 Institute of Mathematical Statistics
, 2001
"... In principle, the Bayesian approach to model selection is straightforward. Prior probability distributions are used to describe the uncertainty surrounding all unknowns. After observing the data, the posterior distribution provides a coherent post data summary of the remaining uncertainty which is r ..."
Abstract

Cited by 94 (3 self)
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In principle, the Bayesian approach to model selection is straightforward. Prior probability distributions are used to describe the uncertainty surrounding all unknowns. After observing the data, the posterior distribution provides a coherent post data summary of the remaining uncertainty which is relevant for model selection. However, the practical implementation of this approach often requires carefully tailored priors and novel posterior calculation methods. In this article, we illustrate some of the fundamental practical issues that arise for two different model selection problems: the variable selection problem for the linear model and the CART model selection problem.
Bayesian Learning in Undirected Graphical Models: Approximate MCMC algorithms
, 2004
"... Bayesian learning in undirected graphical models  computing posterior distributions over parameters and predictive quantities  is exceptionally difficult. We conjecture that for general undirected models, there are no tractable MCMC (Markov Chain Monte Carlo) schemes giving the correct equilib ..."
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Cited by 36 (2 self)
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Bayesian learning in undirected graphical models  computing posterior distributions over parameters and predictive quantities  is exceptionally difficult. We conjecture that for general undirected models, there are no tractable MCMC (Markov Chain Monte Carlo) schemes giving the correct equilibrium distribution over parameters. While this intractability, due to the partition function, is familiar to those performing parameter optimisation, Bayesian learning of posterior distributions over undirected model parameters has been unexplored and poses novel challenges. We propose several approximate MCMC schemes and test on fully observed binary models (Boltzmann machines) for a small coronary heart disease data set and larger artificial systems. While approximations must perform well on the model, their interaction with the sampling scheme is also important. Samplers based on variational meanfield approximations generally performed poorly, more advanced methods using loopy propagation, brief sampling and stochastic dynamics lead to acceptable parameter posteriors. Finally, we demonstrate these techniques on a Markov random field with hidden variables.
Bayesian Testing and Estimation of Association in a TwoWay Contingency Table
, 1996
"... In a twoway contingency table, one is interested in checking the goodness of fit of simple models such as independence, quasiindependence, symmetry, or constant association, and estimating parameters which describe the association structure of the table. In a large table, one may be interested in ..."
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Cited by 2 (0 self)
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In a twoway contingency table, one is interested in checking the goodness of fit of simple models such as independence, quasiindependence, symmetry, or constant association, and estimating parameters which describe the association structure of the table. In a large table, one may be interested in detecting a few outlying cells which deviate from the main association pattern in the table. Bayesian tests of the above hypotheses are described using a prior defined on the set of interaction terms of the loglinear model. These tests and associated estimation procedures have several advantages over classical fitting/estimation procedures First, the tests above can give measures of evidence in support of simple hypotheses. Second, the Bayes factors can be used to give estimates of association parameters of the table which allow for uncertainty that the hypothesized model is true. These methods are illustrated for a number of tables. Key words and phrases: Bayes factors, Laplace method, Gib...
Criticism of a Hierarchical Model Using Bayes Factors
, 1996
"... This paper analyzes a data file of heart transplant surgeries performed in the United States over a twoyear period. A Poisson/Gamma exchangeable model is used to learn about the underlying death rates for 94 hospitals. There are concerns about the suitability of this hierarchical model, including t ..."
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This paper analyzes a data file of heart transplant surgeries performed in the United States over a twoyear period. A Poisson/Gamma exchangeable model is used to learn about the underlying death rates for 94 hospitals. There are concerns about the suitability of this hierarchical model, including the need for a hierarchical structure, the existence of outliers, the choice of prior hyperparameters, the need for a covariate in the model, and the manner in which exchangeability was modeled. Each concern motivates the construction of alternative models and Bayes factors are used to compare the existing model with the alternative models. Graphical displays are used to check the sensitivity of the posterior analysis with respect to model perturbations and plots of Bayes factors are used to criticize these perturbations. 1 Introduction 1.1 Heart transplant mortality data Christiansen and Morris (1995) (henceforth referred to as CM) analyze a data file of all heart transplant surgeries pe...
SPARSITY MODELING FOR HIGH DIMENSIONAL SYSTEMS: APPLICATIONS IN GENOMICS AND STRUCTURAL BIOLOGY
"... The availability of very high dimensional data has brought sparsity modeling to the forefront of statistical research in recent years. From complex physical models with hundreds of parameters to DNA microarrays which offer observations in tens to hundreds of thousands of dimensions, separating relev ..."
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The availability of very high dimensional data has brought sparsity modeling to the forefront of statistical research in recent years. From complex physical models with hundreds of parameters to DNA microarrays which offer observations in tens to hundreds of thousands of dimensions, separating relevant and irrelevant parameters is becoming more and more important. This dissertation will focus on innovations in the area of variable and model selection as they pertain to these high dimensional systems. Chapter 1 will discuss work from the literature on the areas of variable and model selection. Chapter 2 will describe an innovation to hierarchical variable selection modeling that corrects errors that stem from assuming incorrectly that multiple thousands of observations are informing about the same distribution. In Chapter 3, we introduce a novel technique for applying variable selection priors to induce sparsity in variance modeling.
Political Analysis Advance Access published February 24, 2007 A Simple DistributionFree Test for Nonnested Model Selection
"... This paper considers a simple distributionfree test for nonnested model selection. The new test is shown to be asymptotically more efficient than the wellknown Vuong test when the distribution of individual loglikelihood ratios is highly peaked. Monte Carlo results demonstrate that for many appli ..."
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This paper considers a simple distributionfree test for nonnested model selection. The new test is shown to be asymptotically more efficient than the wellknown Vuong test when the distribution of individual loglikelihood ratios is highly peaked. Monte Carlo results demonstrate that for many applied research situations, this distribution is indeed highly peaked. The simulation further demonstrates that the proposed test has greater power than the Vuong test under these conditions. The substantive application addresses the effect of domestic political institutions on foreign policy decision making. Do domestic institutions have effects because they hold political leaders accountable, or do they simply promote political norms that shape elite bargaining behavior? The results indicate that the latter model has greater explanatory power. 1
Contents lists available at ScienceDirect Computational Statistics and Data Analysis
"... journal homepage: www.elsevier.com/locate/csda Twoway Bayesian hierarchical phylogenetic models: An application to the coevolution of gp120 and gp41 during and after enfuvirtide ..."
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journal homepage: www.elsevier.com/locate/csda Twoway Bayesian hierarchical phylogenetic models: An application to the coevolution of gp120 and gp41 during and after enfuvirtide