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We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the…

Discrete data are abundant and often arise as counts or rounded data. These data commonly exhibit complex distributional features such as zero-inflation, over-/under-dispersion, boundedness, and heaping, which render many parametric models…

Principal stratification is a widely used framework for addressing post-randomization complications. After using principal stratification to define causal effects of interest, researchers are increasingly turning to finite mixture models to…

We study Bayesian estimation of mixture models and argue in favor of fitting the marginal posterior distribution over component assignments directly, rather than Gibbs sampling from the joint posterior on components and parameters as is…

We consider estimating the parameters of a Gaussian mixture density with a given number of components best representing a given set of weighted samples. We adopt a density interpretation of the samples by viewing them as a discrete Dirac…

We review common situations in Bayesian latent variable models where the prior distribution that a researcher specifies differs from the prior distribution used during estimation. These situations can arise from the positive definite…

Undirected graphical models are applied in genomics, protein structure prediction, and neuroscience to identify sparse interactions that underlie discrete data. Although Bayesian methods for inference would be favorable in these contexts,…

Most algorithms for hyperspectral image unmixing produce point estimates of fractional abundances of the materials to be separated. However, in the absence of reliable ground truth, the ability to perform abundance uncertainty…

This paper presents a new Bayesian collaborative sparse regression method for linear unmixing of hyperspectral images. Our contribution is twofold; first, we propose a new Bayesian model for structured sparse regression in which the…

Bayesian model comparison (BMC) offers a principled probabilistic approach to study and rank competing models. In standard BMC, we construct a discrete probability distribution over the set of possible models, conditional on the observed…

We study full Bayesian procedures for sparse linear regression when errors have a symmetric but otherwise unknown distribution. The unknown error distribution is endowed with a symmetrized Dirichlet process mixture of Gaussians. For the…

Bayesian predictive inference provides a coherent description of entire predictive uncertainty through predictive distributions. We examine several widely used sparsity priors from the predictive (as opposed to estimation) inference…

Previous Bayesian evaluations of the Conway-Maxwell-Poisson (COM-Poisson) distribution have little discussion of non- and weakly-informative priors for the model. While only considering priors with such limited information restricts…

The exponential and the Lomax distributions are widely used in life testing experiments in mixture models. A mixture model of exponential distribution and Lomax distribution is proposed. Parameters of the proposed model are estimated using…

In this paper we take up Bayesian inference in general multivariate stable distributions. We exploit the representation of Matsui and Takemura (2009) for univariate projections, and the representation of the distributions in terms of their…

We prove the weak consistency of the posterior distribution and that of the Bayes estimator for a two-phase piecewise linear regression mdoel where the break-point is unknown. The non-differentiability of the likelihood of the model with…

Robust Bayesian linear regression is a classical but essential statistical tool. Although novel robustness properties of posterior distributions have been proved recently under a certain class of error distributions, their sufficient…

Using Markov chain Monte Carlo to sample from posterior distributions was the key innovation which made Bayesian data analysis practical. Notoriously, however, MCMC is hard to tune, hard to diagnose, and hard to parallelize. This…

Recent work on overfitting Bayesian mixtures of distributions offers a powerful framework for clustering multivariate data using a latent Gaussian model which resembles the factor analysis model. The flexibility provided by overfitting…

In this paper, we show how a complete and exact Bayesian analysis of a parametric mixture model is possible in some cases when components of the mixture are taken from exponential families and when conjugate priors are used. This restricted…