When recovering an unknown signal from noisy measurements, the computational difficulty of performing optimal Bayesian MMSE (minimum mean squared error) inference often necessitates the use of maximum a posteriori (MAP) inference, a special case of regularized M-estimation, as a surrogate. However, MAP is suboptimal in high dimensions, when the number of unknown signal components is similar to ...

The sparse linear model has seen many successful applications in Statistics, Machine Learning, and Computational Biology, such as identification of gene regulatory networks from micro-array expression data. Prior work has either approximated Bayesian inference by expensive Markov chain Monte Carlo, or replaced it by point estimation. We show how to obtain a good approximation to Bayesian analys...

Following a Bayesian statistical inference paradigm, we provide an alternative methodology for analyzing a multivariate logistic regression. We use a multivariate normal prior in the Bayesian analysis. We present a unique Bayes estimator associated with a prior which is admissible. The Bayes estimators of the coefficients of the model are obtained via MCMC methods. The proposed procedure...

Big spatial datasets are very common in scientific problems, such as those involving remote sensing of the earth by satellites, climate-model output, small-area samples from national surveys, and so forth. In this article, our interest lies primarily in very large, non-Gaussian datasets. We consider a hierarchical statistical model consisting of a conditional exponentialfamily model for the dat...

Markov chain Monte Carlo (MCMC) methods, while facilitating the solution of many complex problems in Bayesian inference, are not currently well adapted to the problem of marginal maximum a posteriori (MMAP) estimation, especially when the number of parameters is large. We present here a simple and novel MCMC strategy, called State-Augmentation for Marginal Estimation (SAME), which leads to MMAP...

The detection and estimation of filtered point processes using noisy data is an essential requirement in many seismic, ultrasonic, and nuclear applications. In this paper, we address this joint detection/estimation problem using a Bayesian approach, which allows us to easily include any relevant prior information. Performing Bayesian inference for such a complex model is a challenging computati...

BACKGROUND Leishmaniasis is endemic in 98 countries with an estimated 350 million people at risk and approximately 2 million cases annually. Brazil is one of the most severely affected countries. METHODOLOGY We applied Bayesian geostatistical negative binomial models to analyze reported incidence data of cutaneous and visceral leishmaniasis in Brazil covering a 10-year period (2001-2010). Par...

Density estimation is a central problem in data mining and knowledge discovery , with applications from data visualization and exploratory data analysis to supervised and unsupervised concept learning. This paper presents a simple nonparametric method for univariate density estimation that uses Bayesian inference and the minimum-message length principle to induce appropriate mixture models. Its...