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103
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 1766 (74 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.
Replicated Microarray Data
 Statistica Sinica
, 2001
"... cDNA microarrays permit us to study the expression of thousands of genes simultaneously. They are now used in many dierent contexts to compare mRNA levels between two or more samples of cells. Microarray experiments typically give us expression measurements on a large number of genes, say 10,00020, ..."
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Cited by 209 (9 self)
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cDNA microarrays permit us to study the expression of thousands of genes simultaneously. They are now used in many dierent contexts to compare mRNA levels between two or more samples of cells. Microarray experiments typically give us expression measurements on a large number of genes, say 10,00020,000, but with few, if any replicates for each gene. Traditional methods using means and standard deviations to detect dierential expression are not completely satisfactory in this context, and so a dierent approach seems desirable. In this paper we present an empirical Bayes method for analysing replicated microarray data. Data from all the genes in a replicate set of experiments are combined into estimates of parameters of a prior distribution. These parameter estimates are then combined at the gene level with means and standard deviations to form a statistic B which can be used to decide whether dierential expression has occurred. The statistic B avoids the problems of using averages or tstatistics. The method is illustrated using data from an experiment comparing the expression of genes in the livers of SRBI transgenic mice with that of the corresponding wildtype mice. In addition we present the results of a simulation study estimating the ROC curve of B and three other statistics for determining dierential expression: the average and two simple modications of the usual tstatistic. B was found to be the most powerful of the four, though the margin was not great. The data were simulated to resemble the SRBI data. Keywords: cDNA microarray, dierential expression, empirical Bayes, replication, ROC curve, tstatistic Department of Mathematics, Uppsala University y Correspondence should be addressed to Ingrid Lonnstedt, telephone/fax +46184712842/4713201, e...
Improving predictive inference under covariate shift by weighting the loglikelihood function
 JOURNAL OF STATISTICAL PLANNING AND INFERENCE
, 2000
"... ..."
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 ..."
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Cited by 121 (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
Density Forecasting: A Survey
 Journal of Forecasting
, 2000
"... A density forecast of the realization of a random variable at some future time is an estimate of the probability distribution of the possible future values of that variable. This chapter presents a selective survey of applications of density forecasting in macroeconomics and finance, and discusses s ..."
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Cited by 104 (11 self)
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A density forecast of the realization of a random variable at some future time is an estimate of the probability distribution of the possible future values of that variable. This chapter presents a selective survey of applications of density forecasting in macroeconomics and finance, and discusses some issues concerning the production, presentation, and evaluation of density forecasts. This chapter first appeared as an article with the same title in Journal of Forecasting, 19 (2000), 235254. The helpful comments and suggestions of Frank Diebold, Stewart Hodges and two anonymous referees are gratefully acknowledged. Subsequent editorial changes have been made following suggestions from the editors of this volume. Responsibility for errors remains with the authors. 2 1. INTRODUCTION A density forecast of the realization of a random variable at some future time is an estimate of the probability distribution of the possible future values of that variable. It thus provides a complet...
Predictive Model Selection
 Journal of the Royal Statistical Society, Ser. B
, 1995
"... this article we propose three criteria that can be used to address model selection. These emphasize observables rather than parameters and are based on a certain Bayesian predictive density. They have a unifying basis that is simple and interpretable,are free of asymptotic de#nitions,and allow the i ..."
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Cited by 97 (5 self)
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this article we propose three criteria that can be used to address model selection. These emphasize observables rather than parameters and are based on a certain Bayesian predictive density. They have a unifying basis that is simple and interpretable,are free of asymptotic de#nitions,and allow the incorporation of prior information. Moreover,two of these criteria are readily calibrated.
Individuation, counting, and statistical inference: The role of frequency and wholeobject representations in judgment under uncertainty
 Journal of Experimental Psychology: General
, 1998
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A survey of online failure prediction methods
 ACM Computing Surveys
, 2010
"... With evergrowing complexity and dynamicity of computer systems, proactive fault management is an effective approach to enhancing availability. Online failure prediction is the key to such techniques. In contrast to classical reliability methods, online failure prediction is based on runtime monitor ..."
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Cited by 37 (1 self)
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With evergrowing complexity and dynamicity of computer systems, proactive fault management is an effective approach to enhancing availability. Online failure prediction is the key to such techniques. In contrast to classical reliability methods, online failure prediction is based on runtime monitoring and a variety of models and methods that use the current state of a system and, frequently, the past experience as well. This survey describes these methods. To capture the wide spectrum of approaches concerning this area, a taxonomy has been developed, whose different approaches are explained and major concepts are described in detail.
Recalibrating Software Reliability Models
 IEEE Transactions on Software Engineering
, 1990
"... In spite of much research effort, there is no universally applicable software reliability growth model which can be trusted to give accurate predictions of reliability in all circumstances. Worse, we are not even in a position to be abl _ to decide a priori which of the many models is most suitable ..."
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Cited by 37 (8 self)
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In spite of much research effort, there is no universally applicable software reliability growth model which can be trusted to give accurate predictions of reliability in all circumstances. Worse, we are not even in a position to be abl _ to decide a priori which of the many models is most suitable in a particular context. Our own r_ecent work has tried to resolve this problem by developing techniqueswhereby, for eccch program, the accuracy of various models can be analysed. A user is thus enabled to select that model which is giving the most accurate reliability predictfons for the particular program under examination. One_of these ways of analysing predictive accuracy, which we callthe uplot, in fact allows a user to estimate the relationship between the predicted reliability and the true reliability. In this paper we show how this can be used to improve reliability predictions in a completely general way by a process of recalibration. Simulation results show that the technique gives improved reliability predictions in a large proportion of cases. However, a user does not need to trust the efficacy of recalibration, since the new reliability estimates produced by the technique are truly predictive and so their accuracy in a particular application can be judged using the earlier methods. The generality of this approach would therefore suggest that it be applied as a matter of course whenever a software reliability model is used. (NASACR186407) RECALl BRATING
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 37 (5 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.