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Multivariate Bayesian error-in-variable (EIV) linear regression is considered to account for additional additive Gaussian error in the features and response. A 3-variable deterministic scan Gibbs samplers is constructed for multivariate EIV…

Bayesian methods for learning Gaussian graphical models offer a principled framework for quantifying model uncertainty and incorporating prior knowledge. However, their scalability is constrained by the computational cost of jointly…

The generalized inverse Gaussian, denoted $\mathrm{GIG}(p, a, b)$, is a flexible family of distributions that includes the gamma, inverse gamma, and inverse Gaussian distributions as special cases. In addition to its applications in…

Gaussian random fields play an important role in many areas of science and engineering. In practice, they are often simulated by sampling from a high-dimensional multivariate normal distribution, which arises from the discretisation of a…

We consider local Markov chain Monte-Carlo algorithms for sampling from the weighted distribution of independent sets with activity $\l$, where the weight of an independent set $I$ is $\l^{|I|}$. A recent result has established that Gibbs…

P-splines provide a flexible setting for modeling nonlinear model components based on a discretized penalty structure with a relatively simple computational backbone. Under a Bayesian inferential framework based on Markov chain Monte Carlo,…

We consider the joint inference of regression coefficients and the inverse covariance matrix for covariates in high-dimensional probit regression, where the predictors are both relevant to the binary response and functionally related to one…

The 21st century has seen an enormous growth in the development and use of approximate Bayesian methods. Such methods produce computational solutions to certain intractable statistical problems that challenge exact methods like Markov chain…

There is wide interest in studying how the distribution of a continuous response changes with a predictor. We are motivated by environmental applications in which the predictor is the dose of an exposure and the response is a health…

This paper considers how to obtain MCMC quantitative convergence bounds which can be translated into tight complexity bounds in high-dimensional {settings}. We propose a modified drift-and-minorization approach, which establishes…

This book aims to provide a graduate-level introduction to advanced topics in Markov chain Monte Carlo (MCMC) algorithms, as applied broadly in the Bayesian computational context. Most, if not all of these topics (stochastic gradient MCMC,…

We introduce and characterise the performance of the Markov chain Monte Carlo (MCMC) inference method Prune Sampling for discrete and deterministic Bayesian networks (BNs). We developed a procedure to obtain the performance of a MCMC…

One of the most demanding calculations is to generate random samples from a specified probability distribution (usually with an unknown normalizing prefactor) in a high-dimensional configuration space. One often has to resort to using a…

In this paper we present a novel methodology to perform Bayesian model selection in linear models with heavy-tailed distributions. We consider a finite mixture of distributions to model a latent variable where each component of the mixture…

Sampling from a lattice Gaussian distribution is emerging as an important problem in various areas such as coding and cryptography. The default sampling algorithm --- Klein's algorithm yields a distribution close to the lattice Gaussian…

Markov chain Monte Carlo (MCMC) algorithms have become powerful tools for Bayesian inference. However, they do not scale well to large-data problems. Divide-and-conquer strategies, which split the data into batches and, for each batch, run…

Rank data arises frequently in marketing, finance, organizational behavior, and psychology. Most analysis of rank data reported in the literature assumes the presence of one or more variables (sometimes latent) based on whose values the…

We consider the problem of scalable sampling algorithms to fit Bayesian generalized linear mixed models on large datasets. Stochastic gradient Langevin dynamics, coupled with smooth re-parameterizations of variance parameters, produces…

We study the rate of Bayesian consistency for hierarchical priors consisting of prior weights on a model index set and a prior on a density model for each choice of model index. Ghosal, Lember and Van der Vaart [2] have obtained general…

Methods for Bayesian simulation in the presence of computationally intractable likelihood functions are of growing interest. Termed likelihood-free samplers, standard simulation algorithms such as Markov chain Monte Carlo have been adapted…