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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… (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. Hyperparameter settings which base selection on… (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 adaptive… (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)

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)

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)

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 numbers… (More)

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) element if "xed at 1 and it is possible to draw from the posterior using standard distributions.… (More)

Researchers have long struggled to identify causal effects in non-experimental settings. Many recently-proposed strategies assume ignorability of the treatment assignment mechanism and require fitting two models – one for the assignment mechanism and one for the response surface. We propose a strategy that instead focuses on very flexibly modeling just the… (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)