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43
Benchmark Priors for Bayesian Model Averaging
 FORTHCOMING IN THE JOURNAL OF ECONOMETRICS
, 2001
"... In contrast to a posterior analysis given a particular sampling model, posterior model probabilities in the context of model uncertainty are typically rather sensitive to the specification of the prior. In particular, “diffuse” priors on modelspecific parameters can lead to quite unexpected consequ ..."
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Cited by 171 (5 self)
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In contrast to a posterior analysis given a particular sampling model, posterior model probabilities in the context of model uncertainty are typically rather sensitive to the specification of the prior. In particular, “diffuse” priors on modelspecific parameters can lead to quite unexpected consequences. Here we focus on the practically relevant situation where we need to entertain a (large) number of sampling models and we have (or wish to use) little or no subjective prior information. We aim at providing an “automatic” or “benchmark” prior structure that can be used in such cases. We focus on the Normal linear regression model with uncertainty in the choice of regressors. We propose a partly noninformative prior structure related to a Natural Conjugate gprior specification, where the amount of subjective information requested from the user is limited to the choice of a single scalar hyperparameter g0j. The consequences of different choices for g0j are examined. We investigate theoretical properties, such as consistency of the implied Bayesian procedure. Links with classical information criteria are provided. More importantly, we examine the finite sample implications of several choices of g0j in a simulation study. The use of the MC3 algorithm of Madigan and York (1995), combined with efficient coding in Fortran, makes it feasible to conduct large simulations. In addition to posterior criteria, we shall also compare the predictive performance of different priors. A classic example concerning the economics of crime will also be provided and contrasted with results in the literature. The main findings of the paper will lead us to propose a “benchmark” prior specification in a linear regression context with model uncertainty.
Bayesian model averaging
 STAT.SCI
, 1999
"... Standard statistical practice ignores model uncertainty. Data analysts typically select a model from some class of models and then proceed as if the selected model had generated the data. This approach ignores the uncertainty in model selection, leading to overcon dent inferences and decisions tha ..."
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Cited by 61 (1 self)
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Standard statistical practice ignores model uncertainty. Data analysts typically select a model from some class of models and then proceed as if the selected model had generated the data. This approach ignores the uncertainty in model selection, leading to overcon dent inferences and decisions that are more risky than one thinks they are. Bayesian model averaging (BMA) provides a coherent mechanism for accounting for this model uncertainty. Several methods for implementing BMA haverecently emerged. We discuss these methods and present anumber of examples. In these examples, BMA provides improved outofsample predictive performance. We also provide a catalogue of
Bayesian information criterion for censored survival models
 Biometrics
"... We investigate the Bayesian Information Criterion (BIC) for variable selection in models for censored survival data. Kass and Wasserman (1995) showed that BIC provides a close approximation to the Bayes factor when a unitinformation prior on the parameter space is used. We propose a revision of the ..."
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Cited by 35 (2 self)
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We investigate the Bayesian Information Criterion (BIC) for variable selection in models for censored survival data. Kass and Wasserman (1995) showed that BIC provides a close approximation to the Bayes factor when a unitinformation prior on the parameter space is used. We propose a revision of the penalty term in BIC so that it is de ned in terms of the number of uncensored events instead of the number of observations. For the simplest censored data model, that of exponential distributions of survival times (i.e. a constant hazard rate), this revision results in a better approximation to the exact Bayes factor based on a conjugate unitinformation prior. In the Cox proportional hazards regression model, we propose de ning BIC in terms of the maximized partial likelihood. Using the number of deaths rather than the number of individuals in the BIC penalty term corresponds to a more realistic prior on the parameter space, and is shown to improve predictive performance for assessing stroke risk in the Cardiovascular Health Study.
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 35 (9 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 Analysis For Simulation Input And Output
, 1997
"... The paper summarizes some important results at the intersection of the fields of Bayesian statistics and stochastic simulation. Two statistical analysis issues for stochastic simulation are discussed in further detail from a Bayesian perspective. First, a review of recent work in input distribution ..."
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Cited by 27 (9 self)
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The paper summarizes some important results at the intersection of the fields of Bayesian statistics and stochastic simulation. Two statistical analysis issues for stochastic simulation are discussed in further detail from a Bayesian perspective. First, a review of recent work in input distribution selection is presented. Then, a new Bayesian formulation for the problem of output analysis for a single system is presented. A key feature is analyzing simulation output as a random variable whose parameters are an unknown function of the simulation's inputs. The distribution of those parameters is inferred from simulation output via Bayesian responsesurface methods. A brief summary of Bayesian inference and decision making is included for reference.
Bayesian Variable Selection and the SwendsenWang Algorithm
"... The need to explore model uncertainty in linear regression models with many predictors has motivated improvements in Markov chain Monte Carlo sampling algorithms for Bayesian variable selection. Currently used sampling algorithms for Bayesian variable selection may perform poorly when there are seve ..."
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Cited by 24 (0 self)
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The need to explore model uncertainty in linear regression models with many predictors has motivated improvements in Markov chain Monte Carlo sampling algorithms for Bayesian variable selection. Currently used sampling algorithms for Bayesian variable selection may perform poorly when there are severe multicollinearities among the predictors. This article describes a new sampling method based on an analogy with the SwendsenWang algorithm for the Ising model, and which can give substantial improvements over alternative sampling schemes in the presence of multicollinearity. In linear regression with a given set of potential predictors we can index possible models by a binary parameter vector that indicates which of the predictors are included or excluded. By thinking of the posterior distribution of this parameter as a binary spatial field, we can use auxiliary variable methods inspired by the SwendsenWang algorithm for the Ising model to sample from the posterior where dependence among parameters is reduced by conditioning on auxiliary variables. Performance of the method is described for both simulated and real data.
Variable selection for nonparametric Gaussian process priors: Models and computational strategies
 Statistical Science
, 2011
"... Abstract. This paper presents a unified treatment of Gaussian process models that extends to data from the exponential dispersion family and to survival data. Our specific interest is in the analysis of data sets with predictors that have an a priori unknown form of possibly nonlinear associations t ..."
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Cited by 13 (0 self)
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Abstract. This paper presents a unified treatment of Gaussian process models that extends to data from the exponential dispersion family and to survival data. Our specific interest is in the analysis of data sets with predictors that have an a priori unknown form of possibly nonlinear associations to the response. The modeling approach we describe incorporates Gaussian processes in a generalized linear model framework to obtain a class of nonparametric regression models where the covariance matrix depends on the predictors. We consider, in particular, continuous, categorical and count responses. We also look into models that account for survival outcomes. We explore alternative covariance formulations for the Gaussian process prior and demonstrate the flexibility of the construction. Next, we focus on the important problem of selecting variables from the set of possible predictors and describe a general framework that employs mixture priors. We compare alternative MCMC strategies for posterior inference and achieve a computationally efficient and practical approach. We demonstrate performances on simulated and benchmark data sets. Key words and phrases: Bayesian variable selection, generalized linear models, Gaussian processes, latent variables, MCMC, nonparametric regression, survival data.
Assessment of Response Bias in Mild Head Injury: Beyond Malingering Tests
"... The evaluation of response bias and malingering in cases of mild head injury should not rely on a single test. Initial injury severity, typical neuropsychological test performance patterns, preexisting emotional stress or chronic social difficulties, history of previous neurologic or psychiatric dis ..."
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Cited by 10 (0 self)
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The evaluation of response bias and malingering in cases of mild head injury should not rely on a single test. Initial injury severity, typical neuropsychological test performance patterns, preexisting emotional stress or chronic social difficulties, history of previous neurologic or psychiatric disorder, other system injuries sustained in the accident, preinjury alcohol abuse, and a propensity to attribute benign cognitive and somatic symptoms to a brain injury must be considered along with performances on measures of response bias. Empirically supported tests and indices are reviewed. Use of the likelihood ratio in diagnosis is shown. Bayesian model averaging as a statistical technique to derive optimal prediction models is demonstrated with a clinical data set. Assessment of Response Bias 3 Assessment of Response Bias in Mild Head Injury: Beyond Malingering Tests Paralleling the increased interest in mild traumatic brain injury (TBI) and use of neuropsychological evidence in the courtroom, numerous comprehensive reviews of the assessment of response bias and malingering of neuropsychological impairment have appeared in the literature over the past decade (e.g., Etcoff & Kampfer, 1996; Iverson & Binder, 2000; Millis & Putnam, 1996; Nies & Sweet, 1994; Rogers, Harrell, & Liff, 1993). Taking the next step in integrating the quickly expanding literature, Slick, Sherman, and Iverson (1999) recently presented diagnostic criteria for "malingered neurocognitive dysfunction (MND)" that are relevant in the assessment of mild TBI. These diagnostic criteria represent a significant contribution to the field because they present a systematic and coherent set of diagnostic guidelines based on empirical findings. Slick et al. (1999) define MND as "...the volitional exaggeration of...
Unraveling the Fortunes of the Fortunate: An Iterative Bayesian Model Averaging (IBMA) Approach
 Journal of Macroeconomics
, 2007
"... We investigate country heterogeneity in crosscountry growth regressions. In contrast to the previous literature that focuses on lowincome countries, this study also highlights growth determinants in highincome (OECD) countries. We introduce Iterative Bayesian Model Averaging (IBMA) to address not ..."
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Cited by 10 (4 self)
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We investigate country heterogeneity in crosscountry growth regressions. In contrast to the previous literature that focuses on lowincome countries, this study also highlights growth determinants in highincome (OECD) countries. We introduce Iterative Bayesian Model Averaging (IBMA) to address not only potential parameter heterogeneity, but also the model uncertainty inherent in growth regressions. IBMA is essential to our estimation because the simultaneous consideration of model uncertainty and parameter heterogeneity in standard growth regressions increases the number of candidate regressors beyond the processing capacity of ordinary BMA algorithms. Our analysis generates three results that strongly support different dimensions of parameter heterogeneity. First, while a large number of regressors can be identified as growth determinants in NonOECD countries, the same regressors are irrelevant for OECD countries. Second, NonOECD countries and the global sample feature only a handful of common growth determinants. Third, and most devastatingly, the long list of variables included in popular crosscountry datasets does not contain regressors that begin to satisfactorily characterize the basic growth determinants in OECD countries.