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Many scientific and engineering problems require to perform Bayesian inferences for unknowns of infinite dimension. In such problems, many standard Markov Chain Monte Carlo (MCMC) algorithms become arbitrary slow under the mesh refinement,…

Metropolis algorithms for approximate sampling of probability measures on infinite dimensional Hilbert spaces are considered and a generalization of the preconditioned Crank-Nicolson (pCN) proposal is introduced. The new proposal is able to…

Latent Gaussian processes are widely applied in many fields like, statistics, inverse problems and machine learning. A popular method for inference is through the posterior distribution, which is typically carried out by Markov Chain Monte…

Parallel Markov Chain Monte Carlo (pMCMC) algorithms generate clouds of proposals at each step to efficiently resolve a target probability distribution. We build a rigorous foundational framework for pMCMC algorithms that situates these…

Bayesian Neural Networks represent a fascinating confluence of deep learning and probabilistic reasoning, offering a compelling framework for understanding uncertainty in complex predictive models. In this paper, we investigate the use of…

In geostatistics, Gaussian random fields are often used to model heterogeneities of soil or subsurface parameters. To give spatial approximations of these random fields, they are discretized. Then, different techniques of geostatistical…

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…

We study Markov chain Monte Carlo (MCMC) algorithms for target distributions defined on matrix spaces. Such an important sampling problem has yet to be analytically explored. We carry out a major step in covering this gap by developing the…

We describe ergodic properties of some Metropolis-Hastings (MH) algorithms for heavy-tailed target distributions. The analysis usually falls into sub-geometric ergodicity framework but we prove that the mixed preconditioned Crank-Nicolson…

Sampling of sharp posteriors in high dimensions is a challenging problem, especially when gradients of the likelihood are unavailable. In low to moderate dimensions, affine-invariant methods, a class of ensemble-based gradient-free methods,…

Bayesian inverse problems highly rely on efficient and effective inference methods for uncertainty quantification (UQ). Infinite-dimensional MCMC algorithms, directly defined on function spaces, are robust under refinement of physical…

This paper proposes a replica exchange preconditioned Langevin diffusion discretized by the Crank-Nicolson scheme (repCNLD) to handle high-dimensional and multi-modal distribution problems. Sampling from high-dimensional and multi-modal…

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…

Many problems in the physical sciences, machine learning, and statistical inference necessitate sampling from a high-dimensional, multi-modal probability distribution. Markov Chain Monte Carlo (MCMC) algorithms, the ubiquitous tool for this…

Markov Chain Monte Carlo (MCMC) methods are a powerful tool for computation with complex probability distributions. However the performance of such methods is critically dependant on properly tuned parameters, most of which are difficult if…

Many scientific and engineering problems require to perform Bayesian inferences in function spaces, in which the unknowns are of infinite dimension. In such problems, many standard Markov Chain Monte Carlo (MCMC) algorithms become arbitrary…

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…

Markov chain Monte Carlo (MCMC) methods are ubiquitous tools for simulation-based inference in many fields but designing and identifying good MCMC samplers is still an open question. This paper introduces a novel MCMC algorithm, namely,…

Adaptive Markov chain Monte Carlo (MCMC) algorithms, which automatically tune their parameters based on past samples, have proved extremely useful in practice. The self-tuning mechanism makes them `non-Markovian', which means that their…

Markov chain Monte Carlo (MCMC) methods are widely used in machine learning. One of the major problems with MCMC is the question of how to design chains that mix fast over the whole state space; in particular, how to select the parameters…