Related papers: Ergodicity of Approximate MCMC Chains with Applica…

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,…

Markov Chain Monte Carlo (MCMC) techniques are now widely used for cosmological parameter estimation. Chains are generated to sample the posterior probability distribution obtained following the Bayesian approach. An important issue is how…

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 learning in undirected graphical models|computing posterior distributions over parameters and predictive quantities is exceptionally difficult. We conjecture that for general undirected models, there are no tractable MCMC (Markov…

We exhibit an efficient procedure for testing, based on a single long state sequence, whether an unknown Markov chain is identical to or $\varepsilon$-far from a given reference chain. We obtain nearly matching (up to logarithmic factors)…

The growing amount of applications that generate vast amount of data in short time scales render the problem of partial monitoring, coupled with prediction, a rather fundamental one. We study the aforementioned canonical problem under the…

In recent years, methods of approximate parameter estimation have attracted considerable interest in complex problems where exact likelihoods are hard to obtain. In their most basic form, Bayesian methods such as Approximate Bayesian…

Markov chain Monte Carlo (MCMC) algorithms have become powerful tools for Bayesian inference. However, they do not scale well to large-data problems. Divide-and-conquer strategies, which split the data into batches and, for each batch, run…

Accept-reject based Markov chain Monte Carlo (MCMC) algorithms have traditionally utilised acceptance probabilities that can be explicitly written as a function of the ratio of the target density at the two contested points. This feature is…

Stochastic gradient Markov chain Monte Carlo (MCMC) algorithms have received much attention in Bayesian computing for big data problems, but they are only applicable to a small class of problems for which the parameter space has a fixed…

This article describes a method for using optimization to derive efficient independent transition functions for Markov chain Monte Carlo simulations. Our interest is in sampling from a posterior density $\pi(x)$ for problems in which the…

High-dimensional limit theorems have been shown useful to derive tuning rules for finding the optimal scaling in random-walk Metropolis algorithms. The assumptions under which weak convergence results are proved are however restrictive: the…

This article studies the convergence properties of trans-dimensional MCMC algorithms when the total number of models is finite. It is shown that, for reversible and some non-reversible trans-dimensional Markov chains, under mild conditions,…

As modern neural networks get more complex, specifying a model with high predictive performance and sound uncertainty quantification becomes a more challenging task. Despite some promising theoretical results on the true posterior…

A maximum likelihood methodology for a general class of models is presented, using an approximate Bayesian computation (ABC) approach. The typical target of ABC methods are models with intractable likelihoods, and we combine an ABC-MCMC…

Bayesian Neural Networks (BNNs) offer robust uncertainty quantification in model predictions, but training them presents a significant computational challenge. This is mainly due to the problem of sampling multimodal posterior distributions…

Markov chain Monte Carlo (MCMC) is an established approach for uncertainty quantification and propagation in scientific applications. A key challenge in applying MCMC to scientific domains is computation: the target density of interest is…

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…

While MCMC methods have become a main work-horse for Bayesian inference, scaling them to large distributed datasets is still a challenge. Embarrassingly parallel MCMC strategies take a divide-and-conquer stance to achieve this by writing…

A number of machine learning algorithms are using a metric, or a distance, in order to compare individuals. The Euclidean distance is usually employed, but it may be more efficient to learn a parametric distance such as Mahalanobis metric.…