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In many problems, complex non-Gaussian and/or nonlinear models are required to accurately describe a physical system of interest. In such cases, Monte Carlo algorithms are remarkably flexible and extremely powerful approaches to solve such…

Bayesian inference for models that have an intractable partition function is known as a doubly intractable problem, where standard Monte Carlo methods are not applicable. The past decade has seen the development of auxiliary variable Monte…

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…

We develop a modular approach to Markov chain Monte Carlo (MCMC) sampling for unnormalized target densities. In this approach, Markov chains are constructed in parallel, each constrained to a subset of the target space. The Monte Carlo…

Markov chain Monte Carlo (MCMC) methods form one of the algorithmic foundations of Bayesian inverse problems. The recent development of likelihood-informed subspace (LIS) methods offers a viable route to designing efficient MCMC methods for…

The rapid development of computing power and efficient Markov Chain Monte Carlo (MCMC) simulation algorithms have revolutionized Bayesian statistics, making it a highly practical inference method in applied work. However, MCMC algorithms…

Increasingly complex datasets pose a number of challenges for Bayesian inference. Conventional posterior sampling based on Markov chain Monte Carlo can be too computationally intensive, is serial in nature and mixes poorly between posterior…

Markov Chain Monte Carlo (MCMC) requires to evaluate the full data likelihood at different parameter values iteratively and is often computationally infeasible for large data sets. In this paper, we propose to approximate the log-likelihood…

We propose a very fast approximate Markov Chain Monte Carlo (MCMC) sampling framework that is applicable to a large class of sparse Bayesian inference problems, where the computational cost per iteration in several models is of order…

Modelling random dynamical systems in continuous time, diffusion processes are a powerful tool in many areas of science. Model parameters can be estimated from time-discretely observed processes using Markov chain Monte Carlo (MCMC) methods…

Sampling from posterior distributions using Markov chain Monte Carlo (MCMC) methods can require an exhaustive number of iterations, particularly when the posterior is multi-modal as the MCMC sampler can become trapped in a local mode for a…

The log Gaussian Cox process is a flexible class of Cox processes, whose intensity surface is stochastic, for incorporating complex spatial and time structure of point patterns. The straightforward inference based on Markov chain Monte…

We construct a new framework for accelerating Markov chain Monte Carlo in posterior sampling problems where standard methods are limited by the computational cost of the likelihood, or of numerical models embedded therein. Our approach…

Sequential Monte Carlo samplers represent a compelling approach to posterior inference in Bayesian models, due to being parallelisable and providing an unbiased estimate of the posterior normalising constant. In this work, we significantly…

Exact approximations of Markov chain Monte Carlo (MCMC) algorithms are a general emerging class of sampling algorithms. One of the main ideas behind exact approximations consists of replacing intractable quantities required to run standard…

We introduce Markov chain Monte Carlo (MCMC) algorithms based on numerical approximations of piecewise-deterministic Markov processes obtained with the framework of splitting schemes. We present unadjusted as well as adjusted algorithms,…

A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems. The algorithm aims to mitigate some of the hurdles faced…

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),…

The modern scale of data has brought new challenges to Bayesian inference. In particular, conventional MCMC algorithms are computationally very expensive for large data sets. A promising approach to solve this problem is embarrassingly…

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…