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16
Model selection and accounting for model uncertainty in graphical models using Occam's window
, 1993
"... We consider the problem of model selection and accounting for model uncertainty in highdimensional contingency tables, motivated by expert system applications. The approach most used currently is a stepwise strategy guided by tests based on approximate asymptotic Pvalues leading to the selection o ..."
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Cited by 265 (46 self)
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We consider the problem of model selection and accounting for model uncertainty in highdimensional contingency tables, motivated by expert system applications. The approach most used currently is a stepwise strategy guided by tests based on approximate asymptotic Pvalues 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 which 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 maximising predictive ability. However, 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 we propose an alternative Bayesian approach that, we contend, takes full account of the true model uncertainty byaveraging overamuch smaller set of models. An efficient search algorithm is developed for nding these models. We consider two classes of graphical models that arise in expert systems: the recursive causal models and the decomposable
Bayesian Model Selection in Social Research (with Discussion by Andrew Gelman & Donald B. Rubin, and Robert M. Hauser, and a Rejoinder)
 SOCIOLOGICAL METHODOLOGY 1995, EDITED BY PETER V. MARSDEN, CAMBRIDGE,; MASS.: BLACKWELLS.
, 1995
"... It is argued that Pvalues and the tests based upon them give unsatisfactory results, especially in large samples. It is shown that, in regression, when there are many candidate independent variables, standard variable selection procedures can give very misleading results. Also, by selecting a singl ..."
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Cited by 256 (19 self)
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It is argued that Pvalues and the tests based upon them give unsatisfactory results, especially in large samples. It is shown that, in regression, when there are many candidate independent variables, standard variable selection procedures can give very misleading results. Also, by selecting a single model, they ignore model uncertainty and so underestimate the uncertainty about quantities of interest. The Bayesian approach to hypothesis testing, model selection and accounting for model uncertainty is presented. Implementing this is straightforward using the simple and accurate BIC approximation, and can be done using the output from standard software. Specific results are presented for most of the types of model commonly used in sociology. It is shown that this approach overcomes the difficulties with P values and standard model selection procedures based on them. It also allows easy comparison of nonnested models, and permits the quantification of the evidence for a null hypothesis...
Bayesian Model Selection and Model Averaging
, 1999
"... This paper reviews the Bayesian approach to model selection and model averaging. In this review, I emphasize objective Bayesian methods based on noninformative priors. I will also discuss implementation details, approximations and relationships to other methods. KEY WORDS AND PHRASES: AIC, Bayes Fac ..."
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Cited by 57 (0 self)
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This paper reviews the Bayesian approach to model selection and model averaging. In this review, I emphasize objective Bayesian methods based on noninformative priors. I will also discuss implementation details, approximations and relationships to other methods. KEY WORDS AND PHRASES: AIC, Bayes Factors, BIC, Consistency, Default Bayes Methods, Markov Chain Monte Carlo.
Bayesian model selection in structural equation models
, 1993
"... A Bayesian approach to model selection for structural equation models is outlined. This enables us to compare individual models, nested or nonnested, and also to search through the (perhaps vast) set of possible models for the best ones. The approach selects several models rather than just one, whe ..."
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Cited by 30 (10 self)
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A Bayesian approach to model selection for structural equation models is outlined. This enables us to compare individual models, nested or nonnested, and also to search through the (perhaps vast) set of possible models for the best ones. The approach selects several models rather than just one, when appropriate, and so enables us to take account, both informally and formally, of uncertainty about model structure when making inferences about quantities of interest. The approach tends to select simpler models than strategies based on multiple Pvaluebased tests. It may thus help to overcome the criticism of structural
Could Fisher, Jeffreys, and Neyman Have Agreed on Testing?
, 2002
"... Ronald Fisher advocated testing using pvalues; Harold Jeffreys proposed use of objective posterior probabilities of hypotheses; and Jerzy Neyman recommended testing with fixed error probabilities. Each was quite critical of the other approaches. ..."
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Cited by 29 (2 self)
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Ronald Fisher advocated testing using pvalues; Harold Jeffreys proposed use of objective posterior probabilities of hypotheses; and Jerzy Neyman recommended testing with fixed error probabilities. Each was quite critical of the other approaches.
Variable selection and Bayesian model averaging in casecontrol studies
, 1998
"... Covariate and confounder selection in casecontrol studies is most commonly carried out using either a twostep method or a stepwise variable selection method in logistic regression. Inference is then carried out conditionally on the selected model, but this ignores the model uncertainty implicit in ..."
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Cited by 19 (7 self)
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Covariate and confounder selection in casecontrol studies is most commonly carried out using either a twostep method or a stepwise variable selection method in logistic regression. Inference is then carried out conditionally on the selected model, but this ignores the model uncertainty implicit in the variable selection process, and so underestimates uncertainty about relative risks. We report on a simulation study designed to be similar to actual casecontrol studies. This shows that pvalues computed after variable selection can greatly overstate the strength of conclusions. For example, for our simulated casecontrol studies with 1,000 subjects, of variables declared to be "significant" with pvalues between.01 and.05, only 49 % actually were risk factors when stepwise variable selection was used. We propose Bayesian model averaging as a formal way of taking account of model uncertainty in casecontrol studies. This yields an easily interpreted summary, the posterior probability that a variable is a risk factor, and our simulation study indicates this to be reasonably well calibrated in the situations simulated. The methods are applied and compared
Bayesian inference procedures derived via the concept of relative surprise
 Communications in Statistics
, 1997
"... of least relative surprise; model checking; change of variable problem; crossvalidation. We consider the problem of deriving Bayesian inference procedures via the concept of relative surprise. The mathematical concept of surprise has been developed by I.J. Good in a long sequence of papers. We make ..."
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Cited by 17 (6 self)
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of least relative surprise; model checking; change of variable problem; crossvalidation. We consider the problem of deriving Bayesian inference procedures via the concept of relative surprise. The mathematical concept of surprise has been developed by I.J. Good in a long sequence of papers. We make a modiÞcation to this development that permits the avoidance of a serious defect; namely, the change of variable problem. We apply relative surprise to the development of estimation, hypothesis testing and model checking procedures. Important advantages of the relative surprise approach to inference include the lack of dependence on a particular loss function and complete freedom to the statistician in the choice of prior for hypothesis testing problems. Links are established with common Bayesian inference procedures such as highest posterior density regions, modal estimates and Bayes factors. From a practical perspective new inference
Replication and meta–analysis in parapsychology (with discussion
 Statistical Science
, 1991
"... Abstract. Parapsychology, the laboratory study of psychic phenomena, has had its history interwoven with that of statistics. Many of the controversies in parapsychology have focused on statistical issues, and statistical models have played an integral role in the experimental work. Recently, parapsy ..."
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Cited by 16 (1 self)
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Abstract. Parapsychology, the laboratory study of psychic phenomena, has had its history interwoven with that of statistics. Many of the controversies in parapsychology have focused on statistical issues, and statistical models have played an integral role in the experimental work. Recently, parapsychologists have been using metaanalysis as a tool for synthesizing large bodies of work. This paper presents an overview of the use of statistics in parapsychology and offers a summary of the metaanalyses that have been conducted. It begins with some anecdotal information about the involvement of statistics and statisticians with the early history of parapsychology. Next, it is argued that most nonstatisticians do not appreciate the connection between power and "successful " replication of experimental effects. Returning to parapsychology, a particular experimental regime is examined by summarizing an extended debate over the interpretation of the results. A new set of experiments designed to resolve the debate is then reviewed. Finally,
Model Selection for Generalized Linear Models via GLIB, with Application to Epidemiology
, 1993
"... Epidemiological studies for assessing risk factors often use logistic regression, loglinear models, or other generalized linear models. They involve many decisions, including the choice and coding of risk factors and control variables. It is common practice to select independent variables using a s ..."
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Cited by 11 (5 self)
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Epidemiological studies for assessing risk factors often use logistic regression, loglinear models, or other generalized linear models. They involve many decisions, including the choice and coding of risk factors and control variables. It is common practice to select independent variables using a series of significance tests and to choose the way variables are coded somewhat arbitrarily. The overall properties of such a procedure are not well understood, and conditioning on a single model ignores model uncertainty, leading to underestimation of uncertainty about quantities of interest (QUOIs). We describe a Bayesian modeling strategy that formalizes the model selection process and propagates model uncertainty through to inference about QUOIs. Each possible combination of modeling decisions defines a different model, and the models are compared using Bayes factors. Inference about a QUOI is based on an average of its posterior distributions under the individual models, weighted by thei...
Type S error rates for classical and Bayesian single and multiple comparison procedures
 COMPUTATIONAL STATISTICS
, 2000
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