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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)
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)
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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)
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 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)