Related papers: Constructing sampling schemes via coupling: Markov…
Optimised lightweight structures, such as shallow domes and slender towers, are prone to sudden buckling failure because geometric uncertainties/imperfections can lead to a drastic reduction in their buckling loads. We introduce a framework…
Auxiliary variable methods such as the Parallel Tempering and the cluster Monte Carlo methods generate samples that follow a target distribution by using proposal and auxiliary distributions. In sampling from complex distributions, these…
We consider the optimal mass transportation problem in $\RR^d$ with measurably parameterized marginals, for general cost functions and under conditions ensuring the existence of a unique optimal transport map. We prove a joint measurability…
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…
A long-standing gap exists between the theoretical analysis of Markov chain Monte Carlo convergence, which is often based on statistical divergences, and the diagnostics used in practice. We introduce the first general convergence…
Traffic dynamics on single or isolated complex networks has been extensively studied in the past decade. Recently, several coupled network models have been developed to describe the interactions between real-world networked systems. In a…
Simplicial complexes are now a popular alternative to networks when it comes to describing the structure of complex systems, primarily because they encode multi-node interactions explicitly. With this new description comes the need for…
The performance of Markov chain Monte Carlo samplers strongly depends on the properties of the target distribution such as its covariance structure, the location of its probability mass and its tail behavior. We explore the use of bijective…
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…
Bayesian sampling is an important task in statistics and machine learning. Over the past decade, many ensemble-type sampling methods have been proposed. In contrast to the classical Markov chain Monte Carlo methods, these new methods deploy…
This article presents an approach to Bayesian semiparametric inference for Gaussian multivariate response regression. We are motivated by various small and medium dimensional problems from the physical and social sciences. The statistical…
Markov jump processes (or continuous-time Markov chains) are a simple and important class of continuous-time dynamical systems. In this paper, we tackle the problem of simulating from the posterior distribution over paths in these models,…
Although multivariate count data are routinely collected in many application areas, there is surprisingly little work developing flexible models for characterizing their dependence structure. This is particularly true when interest focuses…
In the context of Bayesian inversion for scientific and engineering modeling, Markov chain Monte Carlo sampling strategies are the benchmark due to their flexibility and robustness in dealing with arbitrary posterior probability density…
This paper presents a new Markov chain Monte Carlo method to sample from the posterior distribution of conjugate mixture models. This algorithm relies on a flexible split-merge procedure built using the particle Gibbs sampler. Contrary to…
The method of 'coupling from the past' permits exact sampling from the invariant distribution of a Markov chain on a finite state space. The coupling is successful whenever the stochastic dynamics are such that there is coalescence of all…
Describing the complex dependence structure of extreme phenomena is particularly challenging. To tackle this issue we develop a novel statistical algorithm that describes extremal dependence taking advantage of the inherent hierarchical…
This paper focuses on multi-block optimization problems over transport polytopes, which underlie various applications including strongly correlated quantum physics and machine learning. Conventional block coordinate descent-type methods for…
Testing between hypotheses, when independent sampling is possible, is a well developed subject. In this paper, we propose hypothesis tests that are applicable when the samples are obtained using Markov chain Monte Carlo. These tests are…
In this review paper, we describe the use of couplings in several different mathematical problems. We consider the total variation norm, maximal coupling, and the $\bar{d}$-distance. We present a detailed proof of a result recently proved:…