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50
Bayes Factors
, 1995
"... In a 1935 paper, and in his book Theory of Probability, Jeffreys developed a methodology for quantifying the evidence in favor of a scientific theory. The centerpiece was a number, now called the Bayes factor, which is the posterior odds of the null hypothesis when the prior probability on the null ..."
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Cited by 981 (70 self)
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In a 1935 paper, and in his book Theory of Probability, Jeffreys developed a methodology for quantifying the evidence in favor of a scientific theory. The centerpiece was a number, now called the Bayes factor, which is the posterior odds of the null hypothesis when the prior probability on the null is onehalf. Although there has been much discussion of Bayesian hypothesis testing in the context of criticism of P values, less attention has been given to the Bayes factor as a practical tool of applied statistics. In this paper we review and discuss the uses of Bayes factors in the context of five scientific applications in genetics, sports, ecology, sociology and psychology.
Bayes factors and model uncertainty
 DEPARTMENT OF STATISTICS, UNIVERSITY OFWASHINGTON
, 1993
"... In a 1935 paper, and in his book Theory of Probability, Jeffreys developed a methodology for quantifying the evidence in favor of a scientific theory. The centerpiece was a number, now called the Bayes factor, which is the posterior odds of the null hypothesis when the prior probability on the null ..."
Abstract

Cited by 89 (6 self)
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In a 1935 paper, and in his book Theory of Probability, Jeffreys developed a methodology for quantifying the evidence in favor of a scientific theory. The centerpiece was a number, now called the Bayes factor, which is the posterior odds of the null hypothesis when the prior probability on the null is onehalf. Although there has been much discussion of Bayesian hypothesis testing in the context of criticism of Pvalues, less attention has been given to the Bayes factor as a practical tool of applied statistics. In this paper we review and discuss the uses of Bayes factors in the context of five scientific applications. The points we emphasize are: from Jeffreys's Bayesian point of view, the purpose of hypothesis testing is to evaluate the evidence in favor of a scientific theory; Bayes factors offer a way of evaluating evidence in favor ofa null hypothesis; Bayes factors provide a way of incorporating external information into the evaluation of evidence about a hypothesis; Bayes factors are very general, and do not require alternative models to be nested; several techniques are available for computing Bayes factors, including asymptotic approximations which are easy to compute using the output from standard packages that maximize likelihoods; in "nonstandard " statistical models that do not satisfy common regularity conditions, it can be technically simpler to calculate Bayes factors than to derive nonBayesian significance
Model Choice: A Minimum Posterior Predictive Loss Approach
, 1998
"... Model choice is a fundamental and much discussed activity in the analysis of data sets. Hierarchical models introducing random effects can not be handled by classical methods. Bayesian approaches using predictive distributions can, though the formal solution, which includes Bayes factors as a specia ..."
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Cited by 59 (10 self)
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Model choice is a fundamental and much discussed activity in the analysis of data sets. Hierarchical models introducing random effects can not be handled by classical methods. Bayesian approaches using predictive distributions can, though the formal solution, which includes Bayes factors as a special case, can be criticized. We propose a predictive criterion where the goal is good prediction of a replicate of the observed data but tempered by fidelity to the observed values. We obtain this criterion by minimizing posterior loss for a given model and then, for models under consideration, select the one which minimizes this criterion. For a broad range of losses, the criterion emerges approximately as a form partitioned into a goodnessoffit term and a penalty term. In the context of generalized linear mixed effects models we obtain a penalized deviance criterion comprised of a piece which is a Bayesian deviance measure and a piece which is a penalty for model complexity. We illustrate ...
Consistent Model Specification Tests
 Journal of Econometrics
, 1982
"... This paper reviews the literature on tests for the correct specification of the functional form of parametric conditional expectation and conditional distribution models. In particular I will discuss various versions of the Integrated Conditional Moment (ICM) test and the ideas behind them. 1 ..."
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Cited by 49 (10 self)
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This paper reviews the literature on tests for the correct specification of the functional form of parametric conditional expectation and conditional distribution models. In particular I will discuss various versions of the Integrated Conditional Moment (ICM) test and the ideas behind them. 1
2006b, Estimation and model selection of semiparametric copulabased multivariate dynamic models under copula misspeci…cation
 Journal of Econometrics
"... Recently Chen and Fan (2003a) introduced a new class of semiparametric copulabased multivariate dynamic (SCOMDY) models. A SCOMDY model specifies the conditional mean and the conditional variance of a multivariate time series parametrically (such as VAR, GARCH), but specifies the multivariate distr ..."
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Cited by 28 (4 self)
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Recently Chen and Fan (2003a) introduced a new class of semiparametric copulabased multivariate dynamic (SCOMDY) models. A SCOMDY model specifies the conditional mean and the conditional variance of a multivariate time series parametrically (such as VAR, GARCH), but specifies the multivariate distribution of the standardized innovation semiparametrically as a parametric copula evaluated at nonparametric marginal distributions. In this paper, we first study large sample properties of the estimators of SCOMDY model parameters under amisspecified parametric copula, and then establish pseudo likelihood ratio (PLR) tests for model selection between two SCOMDY models with possibly misspecified copulas. Finally we develop PLR tests for model selection between more than two SCOMDY models along the lines of the reality check of White (2000). The limiting distributions of the estimators of copula parameters and the PLR tests do not depend on the estimation of conditional mean and conditional variance parameters. Although the tests are affected by the estimation of unknown marginal distributions of standardized innovations, they have standard parametric rates and the limiting null distributions are very easy to simulate. Empirical applications to multiple
Coevolving protein residues: maximum likelihood identification and relationship to structure
 J. Mol. Biol
, 1999
"... There has been a great deal of recent research on ..."
Assessing model mimicry using the parametric bootstrap
 Journal of Mathematical Psychology
, 2004
"... We present a general sampling procedure to quantify model mimicry, defined as the ability of a model to account for data generated by a competing model. This sampling procedure, called the parametric bootstrap crossfitting method (PBCM; cf. Williams (J. R. Statist. Soc. B 32 (1970) 350; Biometrics ..."
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Cited by 19 (3 self)
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We present a general sampling procedure to quantify model mimicry, defined as the ability of a model to account for data generated by a competing model. This sampling procedure, called the parametric bootstrap crossfitting method (PBCM; cf. Williams (J. R. Statist. Soc. B 32 (1970) 350; Biometrics 26 (1970) 23)), generates distributions of differences in goodnessoffit expected under each of the competing models. In the data informed version of the PBCM, the generating models have specific parameter values obtained by fitting the experimental data under consideration. The data informed difference distributions can be compared to the observed difference in goodnessoffit to allow a quantification of model adequacy. In the data uninformed version of the PBCM, the generating models have a relatively broad range of parameter values based on prior knowledge. Application of both the data informed and the data uninformed PBCM is illustrated with several examples. r 2003 Elsevier Inc. All rights reserved. 1.
Diagnostic Measures for Model Criticism
 JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
, 1996
"... ... In this article we present the general outlook and discuss general families of elaborations for use in practice; the exponential connection elaboration plays a key role. We then describe model elaborations for use in diagnosing: departures from normality, goodness of fit in generalized linear mo ..."
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Cited by 13 (1 self)
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... In this article we present the general outlook and discuss general families of elaborations for use in practice; the exponential connection elaboration plays a key role. We then describe model elaborations for use in diagnosing: departures from normality, goodness of fit in generalized linear models, and variable selection in regression and outlier detection. We illustrate our approach with two applications.
Bootstrap J Tests of Nonnested Linear Regression Models
 Journal of Econometrics
, 2002
"... The J test for nonnested regression models often overrejects very severely as an asymptotic test. We provide a theoretical analysis which explains why and when it performs badly. This analysis implies that, except in certain extreme cases, the J test will perform very well when bootstrapped. Using s ..."
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Cited by 12 (5 self)
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The J test for nonnested regression models often overrejects very severely as an asymptotic test. We provide a theoretical analysis which explains why and when it performs badly. This analysis implies that, except in certain extreme cases, the J test will perform very well when bootstrapped. Using several methods to speed up the simulations, we obtain extremely accurate Monte Carlo results on the finitesample performance of the bootstrapped J test. These results fully support the predictions of our theoretical analysis, even in contexts where the analysis is not strictly applicable.
Does More Intense Competition Lead to Higher Growth
 CEPR Discussion Paper Series No
, 1999
"... An earlier version of this paper was presented at a conference on “Industrial Organisation and ..."
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Cited by 12 (0 self)
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An earlier version of this paper was presented at a conference on “Industrial Organisation and