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Hierarchical models are versatile tools for joint modeling of data sets arising from different, but related, sources. Fully Bayesian inference may, however, become computationally prohibitive if the source-specific data models are complex,…
Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…
Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…
Gaussian graphical models are widely used to infer dependence structures. Bayesian methods are appealing to quantify uncertainty associated with structural learning, i.e., the plausibility of conditional independence statements given the…
Bayesian estimation is increasingly popular for performing model based inference to support policymaking. These data are often collected from surveys under informative sampling designs where subject inclusion probabilities are designed to…
Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using a…
In this paper, we address the fusion problem in wireless sensor networks, where the cross-correlation between the estimates is unknown. To solve the problem within the Bayesian framework, we assume that the covariance matrix has a prior…
The remarkable generalization performance of large-scale models has been challenging the conventional wisdom of the statistical learning theory. Although recent theoretical studies have shed light on this behavior in linear models and…
Unnormalized (or energy-based) models provide a flexible framework for capturing the characteristics of data with complex dependency structures. However, the application of standard Bayesian inference methods has been severely limited…
Two Bayesian models with different sampling densities are said to be marginally equivalent if the joint distribution of observables and the parameter of interest is the same for both models. We discuss marginal equivalence in the general…
This paper studies the role played by identification in the Bayesian analysis of statistical and econometric models. First, for unidentified models we demonstrate that there are situations where the introduction of a non-degenerate prior…
We propose a methodology for modeling and comparing probability distributions within a Bayesian nonparametric framework. Building on dependent normalized random measures, we consider a prior distribution for a collection of discrete random…
It has become increasingly common to collect high-dimensional binary response data; for example, with the emergence of new sampling techniques in ecology. In smaller dimensions, multivariate probit (MVP) models are routinely used for…
Bayesian inversion is central to the quantification of uncertainty within problems arising from numerous applications in science and engineering. To formulate the approach, four ingredients are required: a forward model mapping the unknown…
In inverse problems, it is widely recognized that the incorporation of a sparsity prior yields a regularization effect on the solution. This approach is grounded on the a priori assumption that the unknown can be appropriately represented…
Inferring dependence structure through undirected graphs is crucial for uncovering the major modes of multivariate interaction among high-dimensional genomic markers that are potentially associated with cancer. Traditionally, conditional…
In this article a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and additionally is robust to overfitting. These are…
In this present work, we discuss the Bayesian inference for the bivariate pseudo-exponential distribution. Initially, we assume independent gamma priors and then pseudo-gamma priors for the pseudo-exponential parameters. We are primarily…
This paper proposes Bayesian mosaic, a parallelizable composite posterior, for scalable Bayesian inference on a broad class of multivariate discrete data models. Sampling is embarrassingly parallel since Bayesian mosaic is a multiplication…
Constraints are a natural choice for prior information in Bayesian inference. In various applications, the parameters of interest lie on the boundary of the constraint set. In this paper, we use a method that implicitly defines a…