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The Markov chain Monte Carlo (MCMC) method is widely used in various fields as a powerful numerical integration technique for systems with many degrees of freedom. In MCMC methods, probabilistic state transitions can be considered as a…

Bayesian inference for factorial hidden Markov models is challenging due to the exponentially sized latent variable space. Standard Monte Carlo samplers can have difficulties effectively exploring the posterior landscape and are often…

Bayesian inference in the physical sciences faces a fundamental challenge: the imperative for high-fidelity physical modeling often clashes with the intrinsic limitations of stochastic sampling algorithms. Complex, high-dimensional…

Bayesian inference is a popular and widely-used approach to infer phylogenies (evolutionary trees). However, despite decades of widespread application, it remains difficult to judge how well a given Bayesian Markov chain Monte Carlo (MCMC)…

Bayesian inference allows us to define a posterior distribution over the weights of a generic neural network (NN). Exact posteriors are usually intractable, in which case approximations can be employed. One such approximation - variational…

In this paper, we address the challenge of Markov Chain Monte Carlo (MCMC) algorithms within the approximate Bayesian Computation (ABC) framework, which often get trapped in local optima due to their inherent local exploration mechanism. We…

Bayesian models have become very popular over the last years in several fields such as signal processing, statistics, and machine learning. Bayesian inference requires the approximation of complicated integrals involving posterior…

Markov Chain Monte Carlo (MCMC) methods have revolutionised Bayesian data analysis over the years by making the direct computation of posterior probability densities feasible on modern workstations. However, the calculation of the prior…

We present a sequential Monte Carlo sampler algorithm for the Bayesian analysis of generalised linear mixed models (GLMMs). These models support a variety of interesting regression-type analyses, but performing inference is often extremely…

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…

For big data analysis, high computational cost for Bayesian methods often limits their applications in practice. In recent years, there have been many attempts to improve computational efficiency of Bayesian inference. Here we propose an…

Markov chain Monte Carlo (MCMC) algorithms are ubiquitous in Bayesian computations. However, they need to access the full data set in order to evaluate the posterior density at every step of the algorithm. This results in a great…

Two of the most significant challenges in uncertainty quantification pertain to the high computational cost for simulating complex physical models and the high dimension of the random inputs. In applications of practical interest, both of…

This paper introduces methodology for performing Bayesian inference sequentially on a sequence of posteriors on spaces of different dimensions. We show how this may be achieved through the use of sequential Monte Carlo (SMC) samplers (Del…

Monte Carlo methods are essential tools for Bayesian inference. Gibbs sampling is a well-known Markov chain Monte Carlo (MCMC) algorithm, extensively used in signal processing, machine learning, and statistics, employed to draw samples from…

We propose a novel reversible jump Markov chain Monte Carlo (MCMC) simulated annealing algorithm to optimize radial basis function (RBF) networks. This algorithm enables us to maximize the joint posterior distribution of the network…

Irreversible and rejection-free Monte Carlo methods, recently developed in Physics under the name Event-Chain and known in Statistics as Piecewise Deterministic Monte Carlo (PDMC), have proven to produce clear acceleration over standard…

Markov Chain Monte Carlo (MCMC) algorithms are commonly used for their versatility in sampling from complicated probability distributions. However, as the dimension of the distribution gets larger, the computational costs for a satisfactory…

A simple and efficient adaptive Markov Chain Monte Carlo (MCMC) method, called the Metropolized Adaptive Subspace (MAdaSub) algorithm, is proposed for sampling from high-dimensional posterior model distributions in Bayesian variable…

Delayed-acceptance Markov chain Monte Carlo (DA-MCMC) samples from a probability distribution via a two-stages version of the Metropolis-Hastings algorithm, by combining the target distribution with a "surrogate" (i.e. an approximate and…