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In many domains, we are interested in analyzing the structure of the underlying distribution, e.g., whether one variable is a direct parent of the other. Bayesian model-selection attempts to find the MAP model and use its structure to…

Markov chain Monte Carlo (MCMC) algorithms are widely used to sample from complicated distributions, especially to sample from the posterior distribution in Bayesian inference. However, MCMC is not directly applicable when facing the doubly…

A wide class of Bayesian models involve unidentifiable random matrices that display rotational ambiguity, with the Gaussian factor model being a typical example. A rich variety of Markov chain Monte Carlo (MCMC) algorithms have been…

We outline a procedure for jointly sampling substitution matrices and multiple sequence alignments, according to an approximate posterior distribution, using an MCMC-based algorithm. This procedure provides an efficient and simple method by…

This article develops a Bayesian approach for estimating panel quantile regression with binary outcomes in the presence of correlated random effects. We construct a working likelihood using an asymmetric Laplace (AL) error distribution and…

This paper presents an improved implicit sampling method for hierarchical Bayesian inverse problems. A widely used approach for sampling posterior distribution is based on Markov chain Monte Carlo (MCMC). However, the samples generated by…

We present a novel technique for tailoring Bayesian quadrature (BQ) to model selection. The state-of-the-art for comparing the evidence of multiple models relies on Monte Carlo methods, which converge slowly and are unreliable for…

Imaging genetics aims to uncover the hidden relationship between imaging quantitative traits (QTs) and genetic markers (e.g. single nucleotide polymorphism (SNP)), and brings valuable insights into the pathogenesis of complex diseases, such…

In this article, we consider Markov chain Monte Carlo(MCMC) algorithms for exploring the intractable posterior density associated with Bayesian probit linear mixed models under improper priors on the regression coefficients and variance…

We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…

Boolean matrix factorisation aims to decompose a binary data matrix into an approximate Boolean product of two low rank, binary matrices: one containing meaningful patterns, the other quantifying how the observations can be expressed as a…

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…

Posterior predictive p-values (ppps) have become popular tools for Bayesian model assessment, being general-purpose and easy to use. However, interpretation can be difficult because their distribution is not uniform under the hypothesis…

Acyclic digraphs are the underlying representation of Bayesian networks, a widely used class of probabilistic graphical models. Learning the underlying graph from data is a way of gaining insights about the structural properties of a…

This paper discusses regularized estimators in the multivariate statistical model as tools naturally arising within a Bayesian framework. First, a link is established between Bayesian estimation and inference under parameter rounding…

In recent years dynamical modelling has been provided with a range of breakthrough methods to perform exact Bayesian inference. However it is often computationally unfeasible to apply exact statistical methodologies in the context of large…

Using a Bayesian network to analyze the causal relationship between nodes is a hot spot. The existing network learning algorithms are mainly constraint-based and score-based network generation methods. The constraint-based method is mainly…

We present a multi-fidelity method for uncertainty quantification of parameter estimates in complex systems, leveraging generative models trained to sample the target conditional distribution. In the Bayesian inference setting, traditional…

Estimating the predictive uncertainty of a Bayesian learning model is critical in various decision-making problems, e.g., reinforcement learning, detecting adversarial attack, self-driving car. As the model posterior is almost always…

Recent advances in biological research have seen the emergence of high-throughput technologies with numerous applications that allow the study of biological mechanisms at an unprecedented depth and scale. A large amount of genomic data is…