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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. American Statistical… (More)

This paper describes and compares various hierarchical mixture prior formulations of variable selection uncertainty in normal linear regression models. These include the nonconjugate SSVS formulation of George and McCulloch (1993), as well as conjugate formulations which allow for analytical simplification. Hyperpa-rameter settings which base selection on… (More)

In this paper we put forward a Bayesian approach for nding CART (classiication and regression tree) models. The two basic components of this approach consist of prior speciication and stochastic search. The basic idea is to have the prior induce a posterior distribution which will guide the stochastic search t o wards more promising CART models. As the… (More)

We develop a Bayesian " sum-of-trees " model where each tree is constrained by a regularization prior to be a weak learner, and fitting and inference are accomplished via an iterative Bayesian backfitting MCMC algorithm that generates samples from a posterior. Effectively, BART is a nonparametric Bayesian regression approach which uses dimensionally… (More)

An important aspect of marketing practice is the targeting of consumer segments for differential promotional activity. The premise of this activity is that there exist distinct segments of homogeneous consumers who can be identified by readily available demographic information. The increased availability of individual consumer panel data open the… (More)

We develop new methods for conducting a finite sample, likelihood-based analysis of the multinomial probit model. Using a variant of the Gibbs sampler, an algorithm is developed to draw from the exact posterior of the multinomial probit model with correlated errors. This approach avoids direct evaluation of the likelihood and, thus, avoids the problems… (More)

In principle, the Bayesian approach to model selection is straightforward. Prior probability distributions are used to describe the uncertainty surrounding all unknowns. After observing the data, the posterior distribution provides a coherent post data summary of the remaining uncertainty which is relevant for model selection. However, the practical… (More)

A useful definition of " big data " is data that is too big to comfortably process on a single machine, either because of processor, memory, or disk bottlenecks. Graphics processing units can alleviate the processor bottleneck, but memory or disk bottlenecks can only be eliminated by splitting data across multiple machines. Communication between large… (More)

We develop a Bayesian " sum-of-trees " model, named BART, where each tree is constrained by a prior to be a weak learner. Fitting and inference are accomplished via an iterative backfitting MCMC algorithm. This model is motivated by ensemble methods in general, and boosting algorithms in particular. Like boosting, each weak learner (i.e., each weak tree)… (More)

A Bayesian analysis of the multinomial probit model with fully identi"ed parameters Abstract We present a new prior and corresponding algorithm for Bayesian analysis of the multinomial probit model. Our new approach places a prior directly on the identi"ed parameter space. The key is the speci"cation of a prior on the covariance matrix so that the (1,1)… (More)