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This paper proposes a new approach to sparse-signal detection called the horseshoe estimator. We show that the horseshoe is a close cousin of the lasso in that it arises from the same class of multivariate scale mixtures of normals, but that it is almost universally superior to the double-exponential prior at handling sparsity. A theoretical framework is(More)
We study the classic problem of choosing a prior distribution for a location parameter β = (β 1 ,. .. , βp) as p grows large. First, we study the standard " global-local shrinkage " approach, based on scale mixtures of normals. Two theorems are presented which characterize certain desirable properties of shrinkage priors for sparse problems. Next, we review(More)
This paper presents a general, fully Bayesian framework for sparse supervised-learning problems based on the horseshoe prior. The horseshoe prior is a member of the family of multivariate scale mixtures of normals, and is therefore closely related to widely used approaches for sparse Bayesian learning, including , among others, Laplacian priors (e.g. the(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)
We develop a simulation-based method for the online updating of Gaussian process regression and classification models. Our method exploits sequential Monte Carlo to produce a thrifty sequential design algorithm, in terms of computational speed, compared to the established MCMC alternative. The latter is less ideal for sequential design since it must be(More)
Particle learning provides a simulation-based approach to sequential Bayesian computation. To sample from a posterior distribution of interest we use an essential state vector together with a predictive and propagation rule to build a resampling-sampling framework. Predictive inference and sequential Bayes factors are a direct by-product. Our approach(More)