Related papers: Metropolis-Hastings transition kernel couplings
The classical Metropolis-Hastings (MH) algorithm can be extended to generate non-reversible Markov chains. This is achieved by means of a modification of the acceptance probability, using the notion of vorticity matrix. The resulting Markov…
There has been a recent surge of interest in coupling methods for Markov chain Monte Carlo algorithms: they facilitate convergence quantification and unbiased estimation, while exploiting embarrassingly parallel computing capabilities.…
We propose a new class of learning algorithms that combines variational approximation and Markov chain Monte Carlo (MCMC) simulation. Naive algorithms that use the variational approximation as proposal distribution can perform poorly…
The Metropolis-Hastings algorithm is a fundamental Markov chain Monte Carlo (MCMC) method for sampling and inference. With the advent of Big Data, distributed and parallel variants of MCMC methods are attracting increased attention. In this…
We study the computational complexity of a Metropolis-Hastings algorithm for Bayesian community detection. We first establish a posterior strong consistency result for a natural prior distribution on stochastic block models under the…
When implementing Markov Chain Monte Carlo (MCMC) algorithms, perturbation caused by numerical errors is sometimes inevitable. This paper studies how perturbation of MCMC affects the convergence speed and Monte Carlo estimation accuracy.…
This article extends weak convergence bounds of Markov transition kernels to convergence bounds on the variance of the Markov kernel applied to Lipschitz functions. In the reversible case, weak convergence rates of the transition kernels…
In this paper, we study the asymptotic variance of sample path averages for inhomogeneous Markov chains that evolve alternatingly according to two different $\pi$-reversible Markov transition kernels $P$ and $Q$. More specifically, our main…
We propose a novel Metropolis-Hastings algorithm to sample uniformly from the space of correlation matrices. Existing methods in the literature are based on elaborated representations of a correlation matrix, or on complex parametrizations…
In this paper, we study dependence coefficients for copula-based Markov chains. We provide new tools to check the convergence rates of mixing coefficients of copula-based Markov chains. We study Markov chains generated by the…
Adaptive and interacting Markov chain Monte Carlo algorithms (MCMC) have been recently introduced in the literature. These novel simulation algorithms are designed to increase the simulation efficiency to sample complex distributions.…
Monte Carlo algorithms are a foundational pillar of modern computational science, yet their effective application hinges on a deep understanding of their performance trade offs. This paper presents a critical analysis of the evolution of…
We introduce a new geometric approach that constructs a transition kernel of Markov chain. Our method always minimizes the average rejection rate and even reduce it to zero in many relevant cases, which cannot be achieved by conventional…
The design of the proposal distributions, and most notably the kernel parameters, are crucial for the performance of Markov chain Monte Carlo (MCMC) rendering. A poor selection of parameters can increase the correlation of the Markov chain…
Monte Carlo algorithms often aim to draw from a distribution $\pi$ by simulating a Markov chain with transition kernel $P$ such that $\pi$ is invariant under $P$. However, there are many situations for which it is impractical or impossible…
The Monte Carlo within Metropolis (MCwM) algorithm, interpreted as a perturbed Metropolis-Hastings (MH) algorithm, provides an approach for approximate sampling when the target distribution is intractable. Assuming the unperturbed Markov…
Global fits of physics models require efficient methods for exploring high-dimensional and/or multimodal posterior functions. We introduce a novel method for accelerating Markov Chain Monte Carlo (MCMC) sampling by pairing a…
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…
We consider Metropolis Hastings MCMC in cases where the log of the ratio of target distributions is replaced by an estimator. The estimator is based on m samples from an independent online Monte Carlo simulation. Under some conditions on…
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…