Related papers: Accelerating MCMC with active subspaces
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…
An efficient simulation-based methodology is proposed for the rolling window estimation of state space models, called particle rolling Markov chain Monte Carlo (MCMC) with double block sampling. In our method, which is based on Sequential…
The availability of data sets with large numbers of variables is rapidly increasing. The effective application of Bayesian variable selection methods for regression with these data sets has proved difficult since available Markov chain…
We introduce a new Markov-Chain Monte Carlo (MCMC) approach designed for efficient sampling of highly correlated and multimodal posteriors. Parallel tempering, though effective, is a costly technique for sampling such posteriors. Our…
In the context of solving inverse problems for physics applications within a Bayesian framework, we present a new approach, Markov Chain Generative Adversarial Neural Networks (MCGANs), to alleviate the computational costs associated with…
Selection among alternative theoretical models given an observed data set is an important challenge in many areas of physics and astronomy. Reversible-jump Markov chain Monte Carlo (RJMCMC) is an extremely powerful technique for performing…
Large, sparse linear systems are pervasive in modern science and engineering, and Krylov subspace solvers are an established means of solving them. Yet convergence can be slow for ill-conditioned matrices, so practical deployments usually…
It has become increasingly easy nowadays to collect approximate posterior samples via fast algorithms such as variational Bayes, but concerns exist about the estimation accuracy. It is tempting to build solutions that exploit approximate…
Markov Chain Monte Carlo (MCMC) methods have become a cornerstone of many modern scientific analyses by providing a straightforward approach to numerically estimate uncertainties in the parameters of a model using a sequence of random…
This article reviews the application of advanced Monte Carlo techniques in the context of Multilevel Monte Carlo (MLMC). MLMC is a strategy employed to compute expectations which can be biased in some sense, for instance, by using the…
Spatial whole-brain Bayesian modeling of task-related functional magnetic resonance imaging (fMRI) is a great computational challenge. Most of the currently proposed methods therefore do inference in subregions of the brain separately or do…
As it has become common to use many computer cores in routine applications, finding good ways to parallelize popular algorithms has become increasingly important. In this paper, we present a parallelization scheme for Markov chain Monte…
Variable selection is a key issue when analyzing high-dimensional data. The explosion of data with large sample sizes and dimensionality brings new challenges to this problem in both inference accuracy and computational complexity. To…
Bayesian inverse problems arise in various scientific and engineering domains, and solving them can be computationally demanding. This is especially the case for problems governed by partial differential equations, where the repeated…
Non-linear state space models are a widely-used class of models for biological, economic, and physical processes. Fitting these models to observed data is a difficult inference problem that has no straightforward solution. We take a…
Markov chain Monte Carlo (MCMC) methods are foundational algorithms for Bayesian inference and probabilistic modeling. However, most MCMC algorithms are inherently sequential and their time complexity scales linearly with the sequence…
Markov chain Monte Carlo (MCMC) sampling is an important and commonly used tool for the analysis of hierarchical models. Nevertheless, practitioners generally have two options for MCMC: utilize existing software that generates a black-box…
Many problems of practical interest rely on Continuous-time Markov chains~(CTMCs) defined over combinatorial state spaces, rendering the computation of transition probabilities, and hence probabilistic inference, difficult or impossible…
Modern imaging methods rely strongly on Bayesian inference techniques to solve challenging imaging problems. Currently, the predominant Bayesian computation approach is convex optimisation, which scales very efficiently to high dimensional…
The widespread use of Markov Chain Monte Carlo (MCMC) methods for high-dimensional applications has motivated research into the scalability of these algorithms with respect to the dimension of the problem. Despite this, numerous problems…