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Bayesian mixture models are widely applied for unsupervised learning and exploratory data analysis. Markov chain Monte Carlo based on Gibbs sampling and split-merge moves are widely used for inference in these models. However, both methods…

We investigate the efficiency of a marginal likelihood estimator where the product of the marginal posterior distributions is used as an importance-sampling function. The approach is generally applicable to multi-block parameter vector…

Many probabilistic models introduce strong dependencies between variables using a latent multivariate Gaussian distribution or a Gaussian process. We present a new Markov chain Monte Carlo algorithm for performing inference in models with…

Model comparison for the purposes of selection, averaging and validation is a problem found throughout statistics. Within the Bayesian paradigm, these problems all require the calculation of the posterior probabilities of models within a…

Reversible jump Markov chain Monte Carlo (RJMCMC) proposals that achieve reasonable acceptance rates and mixing are notoriously difficult to design in most applications. Inspired by recent advances in deep neural network-based normalizing…

We discuss a non-reversible, lifted Markov-chain Monte Carlo (MCMC) algorithm for particle systems in which the direction of proposed displacements is changed deterministically. This algorithm sweeps through directions analogously to the…

In the first part of this paper we study approximations of trajectories of Piecewise Deter-ministic Processes (PDP) when the flow is not explicit by the thinning method. We also establish a strong error estimate for PDPs as well as a weak…

Generalized linear mixed models (GLMMs) are often used for analyzing correlated non-Gaussian data. The likelihood function in a GLMM is available only as a high dimensional integral, and thus closed-form inference and prediction are not…

We extend the hypocoercivity framework for piecewise-deterministic Markov process (PDMP) Monte Carlo established in [Andrieu et. al. (2018)] to heavy-tailed target distributions, which exhibit subgeometric rates of convergence to…

High-dimensional distributions, especially those with heavy tails, are notoriously difficult for off-the-shelf MCMC samplers: the combination of unbounded state spaces, diminishing gradient information, and local moves results in…

The reversible jump Markov chain Monte Carlo (RJMCMC) method offers an across-model simulation approach for Bayesian estimation and model comparison, by exploring the sampling space that consists of several models of possibly varying…

Bayesian shrinkage methods have generated a lot of recent interest as tools for high-dimensional regression and model selection. These methods naturally facilitate tractable uncertainty quantification and incorporation of prior information.…

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…

In general, the statistical simulation approaches are referred to as the Monte Carlo methods as a whole. The broad class of the Monte Carlo methods involves the Markov chain Monte Carlo (MCMC) techniques that attract the attention of…

Markov chain Monte Carlo (MCMC) methods are sampling methods that have become a commonly used tool in statistics, for example to perform Monte Carlo integration. As a consequence of the increase in computational power, many variations of…

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…

Solving ill-posed inverse problems by Bayesian inference has recently attracted considerable attention. Compared to deterministic approaches, the probabilistic representation of the solution by the posterior distribution can be exploited to…

Multiproposal MCMC (MP-MCMC) algorithms use clouds of proposals to efficiently traverse state spaces and overcome complex target geometries. While MCMC methods are embarrassingly parallel by nature, the non-trivial forms of parallelism…

We develop a new method to sample from posterior distributions in hierarchical models without using Markov chain Monte Carlo. This method, which is a variant of importance sampling ideas, is generally applicable to high-dimensional models…

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…