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Philosophy and the practice of Bayesian statistics
, 2010
"... A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the most successful forms of Bayesian statistics do not actually ..."
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Cited by 13 (5 self)
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A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the most successful forms of Bayesian statistics do not actually support that particular philosophy but rather accord much better with sophisticated forms of hypotheticodeductivism. We examine the actual role played by prior distributions in Bayesian models, and the crucial aspects of model checking and model revision, which fall outside the scope of Bayesian confirmation theory. We draw on the literature on the consistency of Bayesian updating and also on our experience of applied work in social science. Clarity about these matters should benefit not just philosophy of science, but also statistical practice. At best, the inductivist view has encouraged researchers to fit and compare models without checking them; at worst, theorists have actively discouraged practitioners from performing model checking because it does not fit into their framework.
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
"... ..."
Selecting The Best System: A DecisionTheoretic Approach
 In Proc. 1997 Winter Simulation Conference
, 1997
"... The problem of selecting the best system from a finite set of alternatives is considered from a Bayesian decisiontheoretic perspective. The framework presented is quite general, and permits selection from two or more systems, with replications that use either independent or common random numbers, w ..."
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Cited by 10 (2 self)
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The problem of selecting the best system from a finite set of alternatives is considered from a Bayesian decisiontheoretic perspective. The framework presented is quite general, and permits selection from two or more systems, with replications that use either independent or common random numbers, with unknown means and covariances for the output, and permits Gaussian or nonGaussian simulation output. For the case of unknown mean and variance with common random numbers, the framework provides a probability of correct selection that does not suffer from problems associated with the Bonferroni inequality. We indicate some criteria for which the Bayesian approach and other approaches are in general agreement, or disagreement. The probability of correct selection can be calculated either by quadrature or by Monte Carlo simulation from the posterior distribution of the parameters of the statistical distribution of the simulation output. We also comment on expectedvalue decisionmaking ver...
Checking for priordata conflict
 Bayesian Analysis
, 2006
"... Abstract. Inference proceeds from ingredients chosen by the analyst and data. To validate any inferences drawn it is essential that the inputs chosen be deemed appropriate for the data. In the Bayesian context these inputs consist of both the sampling model and the prior. There are thus two possibil ..."
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Cited by 10 (7 self)
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Abstract. Inference proceeds from ingredients chosen by the analyst and data. To validate any inferences drawn it is essential that the inputs chosen be deemed appropriate for the data. In the Bayesian context these inputs consist of both the sampling model and the prior. There are thus two possibilities for failure: the data may not have arisen from the sampling model, or the prior may place most of its mass on parameter values that are not feasible in light of the data (referred to here as priordata conflict). Failure of the sampling model can only be fixed by modifying the model, while priordata conflict can be overcome if sufficient data is available. We examine how to assess whether or not a priordata conflict exists, and how to assess when its effects can be ignored for inferences. The concept of priordata conflict is seen to lead to a partial characterization of what is meant by a noninformative prior or a noninformative sequence of priors.
A Bayesian approach to the selection and testing of mixture models
 Statistica Sinica
, 2001
"... Abstract: An important aspect of mixture modeling is the selection of the number of mixture components. In this paper, we discuss the Bayes factor as a selection tool. The discussion will focus on two aspects: computation of the Bayes factor and prior sensitivity. For the computation, we propose a v ..."
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Cited by 9 (3 self)
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Abstract: An important aspect of mixture modeling is the selection of the number of mixture components. In this paper, we discuss the Bayes factor as a selection tool. The discussion will focus on two aspects: computation of the Bayes factor and prior sensitivity. For the computation, we propose a variant of Chib’s estimator that accounts for the nonidentifiability of the mixture components. To reduce the prior sensitivity of the Bayes factor, we propose to extend the model with a hyperprior. We further discuss the use of posterior predictive checks for examining the fit of the model. The ideas are illustrated by means of a psychiatric diagnosis example.
Bayesian Selection of LogLinear Models
 Canadian Journal of Statistics
, 1995
"... A general methodology is presented for finding suitable Poisson loglinear models with applications to multiway contingency tables. Mixtures of multivariate normal distributions are used to model prior opinion when a subset of the regression vector is believed to be nonzero. This prior distribution ..."
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Cited by 7 (2 self)
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A general methodology is presented for finding suitable Poisson loglinear models with applications to multiway contingency tables. Mixtures of multivariate normal distributions are used to model prior opinion when a subset of the regression vector is believed to be nonzero. This prior distribution is studied for two and threeway contingency tables, in which the regression coefficients are interpretable in terms of oddsratios in the table. Efficient and accurate schemes are proposed for calculating the posterior model probabilities. The methods are illustrated for a large number of twoway simulated tables and for two threeway tables. These methods appear to be useful in selecting the best loglinear model and in estimating parameters of interest that reflect uncertainty in the true model. Key words and phrases: Bayes factors, Laplace method, Gibbs sampling, Model selection, Odds ratios. AMS subject classifications: Primary 62H17, 62F15, 62J12. 1 Introduction 1.1 Bayesian testing...
Objective Bayesian analysis of contingency tables
, 2002
"... The statistical analysis of contingency tables is typically carried out with a hypothesis test. In the Bayesian paradigm, default priors for hypothesis tests are typically improper, and cannot be used. Although such priors are available, and proper, for testing contingency tables, we show that for t ..."
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Cited by 6 (2 self)
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The statistical analysis of contingency tables is typically carried out with a hypothesis test. In the Bayesian paradigm, default priors for hypothesis tests are typically improper, and cannot be used. Although such priors are available, and proper, for testing contingency tables, we show that for testing independence they can be greatly improved on by socalled intrinsic priors. We also argue that because there is no realistic situation that corresponds to the case of conditioning on both margins of a contingency table, the proper analysis of an a × b contingency table should only condition on either the table total or on only one of the margins. The posterior probabilities from the intrinsic priors provide reasonable answers in these cases. Examples using simulated and real data are given.
Why Psychologists Must Change the Way They Analyze Their Data: The Case of Psi
"... Does psi exist? In a recent article, Dr. Bem conducted nine studies with over a thousand participants in an attempt to demonstrate that future events retroactively affect people’s responses. Here we discuss several limitations of Bem’s experiments on psi; in particular, we show that the data analysi ..."
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Cited by 6 (1 self)
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Does psi exist? In a recent article, Dr. Bem conducted nine studies with over a thousand participants in an attempt to demonstrate that future events retroactively affect people’s responses. Here we discuss several limitations of Bem’s experiments on psi; in particular, we show that the data analysis was partly exploratory, and that onesided pvalues may overstate the statistical evidence against the null hypothesis. We reanalyze Bem’s data using a default Bayesian ttest and show that the evidence for psi is weak to nonexistent. We argue that in order to convince a skeptical audience of a controversial claim, one needs to conduct strictly confirmatory studies and analyze the results with statistical tests that are conservative rather than liberal. We conclude that Bem’s pvalues do not indicate evidence in favor of precognition; instead, they indicate that experimental psychologists need to change the way they conduct their experiments and analyze their data.
A Bayesian perspective on hypothesis testing  A Comment On Killeen (2005)
 PSYCHOLOGICAL SCIENCE
, 2006
"... In a recent article, Killeen (2005a) proposed an alternative to traditional nullhypothesis significance testing (NHST). This alternative test is based on the statistic p rep, which is the probability of replicating an effect. We share Killeen’s skepticism with respect to nullhypothesis testing, an ..."
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Cited by 5 (0 self)
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In a recent article, Killeen (2005a) proposed an alternative to traditional nullhypothesis significance testing (NHST). This alternative test is based on the statistic p rep, which is the probability of replicating an effect. We share Killeen’s skepticism with respect to nullhypothesis testing, and we sympathize with the proposed conceptual shift toward issues such as replicability. One of the problems associated with NHST is that p values are prone to misinterpretation (cf. Nickerson, 2000, pp. 246– 263). Another problem with NHST is that it can provide highly misleading evidence against the null hypothesis (Killeen, 2005a, p. 345): NHST can lead one to reject the null hypothesis when there is really not enough evidence to do so. Killeen’s prep statistic successfully addresses the problem of misinterpretation, and this is a major contribution (cf. Cumming, 2005; Doros & Geier, 2005; Killeen, 2005b; Macdonald, 2005). However,