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Bayesian inverse problems often involve sampling posterior distributions on infinite-dimensional function spaces. Traditional Markov chain Monte Carlo (MCMC) algorithms are characterized by deteriorating mixing times upon mesh-refinement,…

Markov chain Monte Carlo (MCMC) methods are fundamental to Bayesian computation, but can be computationally intensive, especially in high-dimensional settings. Push-forward generative models, such as generative adversarial networks (GANs),…

In the quest for scalable Bayesian computational algorithms we need to exploit the full potential of existing methodologies. In this note we point out that message passing algorithms, which are very well developed for inference in graphical…

We propose a sequential Markov chain Monte Carlo (SMCMC) algorithm to sample from a sequence of probability distributions, corresponding to posterior distributions at different times in on-line applications. SMCMC proceeds as in usual MCMC…

We present a flexible Bayesian semiparametric mixed model for longitudinal data analysis in the presence of potentially high-dimensional categorical covariates. Building on a novel hidden Markov tensor decomposition technique, our proposed…

Bayesian phylogenetic inference is currently done via Markov chain Monte Carlo (MCMC) with simple proposal mechanisms. This hinders exploration efficiency and often requires long runs to deliver accurate posterior estimates. In this paper,…

Markov chain Monte Carlo (MCMC) methods are frequently used to approximately simulate high-dimensional, multimodal probability distributions. In adaptive MCMC methods, the transition kernel is changed "on the fly" in the hope to speed up…

We analyse the performance of a recursive Monte Carlo method for the Bayesian estimation of the static parameters of a discrete--time state--space Markov model. The algorithm employs two layers of particle filters to approximate the…

Recent advances on overfitting Bayesian mixture models provide a solid and straightforward approach for inferring the underlying number of clusters and model parameters in heterogeneous datasets. The applicability of such a framework in…

Varying coefficient models (VCMs) are widely used for estimating nonlinear regression functions for functional data. Their Bayesian variants using Gaussian process priors on the functional coefficients, however, have received limited…

Optimal designs minimize the number of experimental runs (samples) needed to accurately estimate model parameters, resulting in algorithms that, for instance, efficiently minimize parameter estimate variance. Governed by knowledge of past…

We introduce a Markov Chain Monte Carlo (MCMC) method that is designed to sample from target distributions with irregular geometry using an adaptive scheme. In cases where targets exhibit non-Gaussian behaviour, we propose that adaption…

Classical parameter-space Bayesian inference for Bayesian neural networks (BNNs) suffers from several unresolved prior issues, such as knowledge encoding intractability and pathological behaviours in deep networks, which can lead to…

The generalized linear mixed model (GLMM) is widely used for analyzing correlated data, particularly in large-scale biomedical and social science applications. Scalable Bayesian inference for GLMMs is challenging because the marginal…

In sampling tasks, it is common for target distributions to be known up to a normalizing constant. However, in many situations, even evaluating the unnormalized distribution can be costly or infeasible. This issue arises in scenarios such…

Combined inference for heterogeneous high-dimensional data is critical in modern biology, where clinical and various kinds of molecular data may be available from a single study. Classical genetic association studies regress a single…

A method was developed for Bayesian inference of species phylogeny using the multi-species coalescent model. To improve the mixing properties of the Markov chain Monte Carlo (MCMC) algorithm that traverses the space of species trees, we…

Markov Chain Monte Carlo (MCMC) algorithms are often used for approximate inference inside learning, but their slow mixing can be difficult to diagnose and the approximations can seriously degrade learning. To alleviate these issues, we…

Markov Chain Monte Carlo methods become increasingly popular in applied mathematics as a tool for numerical integration with respect to complex and high-dimensional distributions. However, application of MCMC methods to heavy tailed…

Many Bayesian inference problems require exploring the posterior distribution of high-dimensional parameters that represent the discretization of an underlying function. This work introduces a family of Markov chain Monte Carlo (MCMC)…