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Nonlinear non-Gaussian state-space models arise in numerous applications in statistics and signal processing. In this context, one of the most successful and popular approximation techniques is the Sequential Monte Carlo (SMC) algorithm,…
Markov Chain Monte Carlo (MCMC) is a flexible approach to approximate sampling from intractable probability distributions, with a rich theoretical foundation and comprising a wealth of exemplar algorithms. While the qualitative correctness…
Today, cheap numerical hardware offers huge amounts of parallel computing power, much of which is used for the task of fitting neural networks to data. Adoption of this hardware to accelerate statistical Markov chain Monte Carlo (MCMC)…
Markov chain Monte Carlo is a class of algorithms for drawing Markovian samples from high-dimensional target densities to approximate the numerical integration associated with computing statistical expectation, especially in Bayesian…
It is common practice in Markov chain Monte Carlo to update the simulation one variable (or sub-block of variables) at a time, rather than conduct a single full-dimensional update. When it is possible to draw from each full-conditional…
Inference after model selection presents computational challenges when dealing with intractable conditional distributions. Markov chain Monte Carlo (MCMC) is a common method for sampling from these distributions, but its slow convergence…
Markov Chain Monte Carlo (MCMC) methods sample from unnormalized probability distributions and offer guarantees of exact sampling. However, in the continuous case, unfavorable geometry of the target distribution can greatly limit the…
A fundamental problem in network analysis is clustering the nodes into groups which share a similar connectivity pattern. Existing algorithms for community detection assume the knowledge of the number of clusters or estimate it a priori…
Despite their exceptional flexibility and popularity, the Monte Carlo methods often suffer from slow mixing times for challenging statistical physics problems. We present a general strategy to overcome this difficulty by adopting ideas and…
A novel class of non-reversible Markov chain Monte Carlo schemes relying on continuous-time piecewise-deterministic Markov Processes has recently emerged. In these algorithms, the state of the Markov process evolves according to a…
A novel adaptive Markov chain Monte Carlo algorithm is presented. The algorithm utilizes sparsity in the partial correlation structure of a density to efficiently estimate the covariance matrix through the Cholesky factor of the precision…
Markov chain Monte Carlo (MCMC) sampling of densities restricted to linearly constrained domains is an important task arising in Bayesian treatment of inverse problems in the natural sciences. While efficient algorithms for uniform polytope…
Bayesian inference using Markov Chain Monte Carlo (MCMC) on large datasets has developed rapidly in recent years. However, the underlying methods are generally limited to relatively simple settings where the data have specific forms of…
One of the major problems in adaptive filtering is the problem of system identification. It has been studied extensively due to its immense practical importance in a variety of fields. The underlying goal is to identify the impulse response…
In this paper, we address technical difficulties that arise when applying Markov chain Monte Carlo (MCMC) to hierarchical models designed to perform clustering in the space of latent parameters of subject-wise generative models.…
Probabilistic models help us encode latent structures that both model the data and are ideally also useful for specific downstream tasks. Among these, mixture models and their time-series counterparts, hidden Markov models, identify…
We propose a Markov Chain Monte Carlo (MCMC) algorithm based on Gibbs sampling with parallel tempering to solve nonlinear optimal control problems. The algorithm is applicable to nonlinear systems with dynamics that can be approximately…
Markov chain Monte Carlo (MCMC) algorithms are generally regarded as the gold standard technique for Bayesian inference. They are theoretically well-understood and conceptually simple to apply in practice. The drawback of MCMC is that in…
Many applications in signal processing require the estimation of some parameters of interest given a set of observed data. More specifically, Bayesian inference needs the computation of {\it a-posteriori} estimators which are often…
This review paper, written for the second edition of the Handbook of Markov Chain Monte Carlo, provides an introduction to the study of convergence analysis for Markov chain Monte Carlo (MCMC), aimed at researchers new to the field. We…