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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 ..."
Abstract

Cited by 94 (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.
Objective Bayesian variable selection
 Journal of the American Statistical Association 2006
, 2002
"... A novel fully automatic Bayesian procedure for variable selection in normal regression model is proposed. The procedure uses the posterior probabilities of the models to drive a stochastic search. The posterior probabilities are computed using intrinsic priors, which can be considered default priors ..."
Abstract

Cited by 18 (4 self)
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A novel fully automatic Bayesian procedure for variable selection in normal regression model is proposed. The procedure uses the posterior probabilities of the models to drive a stochastic search. The posterior probabilities are computed using intrinsic priors, which can be considered default priors for model selection problems. That is, they are derived from the model structure and are free from tuning parameters. Thus, they can be seen as objective priors for variable selection. The stochastic search is based on a MetropolisHastings algorithm with a stationary distribution proportional to the model posterior probabilities. The procedure is illustrated on both simulated and real examples.
Temperature Wind
"... ) model (Lewis and Stevens, 1991; Lewis et al., 1994). The modelling is done by letting the predictor variables for the øth value in the time series fy ø g be given by y ø \Gamma1 (= x ø;1 ); y ø \Gamma2 (= x ø;2 ); : : : ; y ø \Gammap (= x ø;p ). Note that if we combined these predictors to form a ..."
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) model (Lewis and Stevens, 1991; Lewis et al., 1994). The modelling is done by letting the predictor variables for the øth value in the time series fy ø g be given by y ø \Gamma1 (= x ø;1 ); y ø \Gamma2 (= x ø;2 ); : : : ; y ø \Gammap (= x ø;p ). Note that if we combined these predictors to form a linear additive function we would just be modelling the time series as a usual AR(p) process. However, the ASTAR method involves modelling these lagged predictors variables using a MARS model. Thus the predictor 5.6. MODELLING TIME SERIES USING BAYESIAN MARS 127 variables can have both threshold terms, because of the form of the truncated linear spline basis functions, and interactions
Aspects of Bayesian Model Choice
"... esentation 2 Information Criteria. Generally, most information criteria select the model that minimize a quantity similar to ICm = \Gamma2log ` f (yj `m ; m) ' + dmF (1) ffl ` m is the parameter vector and ` m are the the MLE. ffl F is the penalty for each additional parameter used in the mo ..."
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esentation 2 Information Criteria. Generally, most information criteria select the model that minimize a quantity similar to ICm = \Gamma2log ` f (yj `m ; m) ' + dmF (1) ffl ` m is the parameter vector and ` m are the the MLE. ffl F is the penalty for each additional parameter used in the model. In linear regression models: ffl ` T m = [fi T (m) ; oe 2 ]. ffl Minimizing \Gamma2log ` f (yj ` m ; m) ' is equivalent to minimizing nlog(RSSm<F43.1
Specification of prior distributions under model uncertainty
, 2008
"... We consider the specification of prior distributions for Bayesian model comparison, focusing on regressiontype models. We propose a particular joint specification of the prior distribution across models so that sensitivity of posterior model probabilities to the dispersion of prior distributions fo ..."
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We consider the specification of prior distributions for Bayesian model comparison, focusing on regressiontype models. We propose a particular joint specification of the prior distribution across models so that sensitivity of posterior model probabilities to the dispersion of prior distributions for the parameters of individual models (Lindley’s paradox) is diminished. We illustrate the behavior of inferential and predictive posterior quantities in linear and loglinear regressions under our proposed prior densities with a series of simulated and real data examples.
Journal of the American Statistical Association is currently published by American Statistical Association.
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Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, noncommercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at