Related papers: When are Unbiased Monte Carlo Estimators More Pref…

Constructing unbiased estimators from Markov chain Monte Carlo (MCMC) outputs is a difficult problem that has recently received a lot of attention in the statistics and machine learning communities. However, the current unbiased MCMC…

Performing numerical integration when the integrand itself cannot be evaluated point-wise is a challenging task that arises in statistical analysis, notably in Bayesian inference for models with intractable likelihood functions. Markov…

We present general principles for the design and analysis of unbiased Monte Carlo estimators in a wide range of settings. Our estimators posses finite work-normalized variance under mild regularity conditions. We apply our estimators to…

We propose a methodology to parallelize Hamiltonian Monte Carlo estimators. Our approach constructs a pair of Hamiltonian Monte Carlo chains that are coupled in such a way that they meet exactly after some random number of iterations. These…

A key quantity of interest in Bayesian inference are expectations of functions with respect to a posterior distribution. Markov Chain Monte Carlo is a fundamental tool to consistently compute these expectations via averaging samples drawn…

Markov chain Monte Carlo (MCMC) methods provide consistent of integrals as the number of iterations goes to infinity. MCMC estimators are generally biased after any fixed number of iterations. We propose to remove this bias by using…

While generally considered computationally expensive, Uncertainty Quantification using Monte Carlo sampling remains beneficial for applications with uncertainties of high dimension. As an extension of the naive Monte Carlo method, the…

We describe an embarrassingly parallel, anytime Monte Carlo method for likelihood-free models. The algorithm starts with the view that the stochasticity of the pseudo-samples generated by the simulator can be controlled externally by a…

Posterior distributions often feature intractable normalizing constants, called marginal likelihoods or evidence, that are useful for model comparison via Bayes factors. This has motivated a number of methods for estimating ratios of…

We provide a general methodology for unbiased estimation for intractable stochastic models. We consider situations where the target distribution can be written as an appropriate limit of distributions, and where conventional approaches…

Markov chain Monte Carlo (MCMC) is a powerful methodology for the approximation of posterior distributions. However, the iterative nature of MCMC does not naturally facilitate its use with modern highly parallel computation on HPC and cloud…

In this article, we consider computing expectations w.r.t. probability measures which are subject to discretization error. Examples include partially observed diffusion processes or inverse problems, where one may have to discretize time…

Multilevel Monte Carlo (MLMC) and unbiased estimators recently proposed by McLeish (Monte Carlo Methods Appl., 2011) and Rhee and Glynn (Oper. Res., 2015) are closely related. This connection is elaborated by presenting a new general class…

We show how to extend a recently proposed multi-level Monte Carlo approach to the continuous time Markov chain setting, thereby greatly lowering the computational complexity needed to compute expected values of functions of the state of the…

This document presents methods to remove the initialization or burn-in bias from Markov chain Monte Carlo (MCMC) estimates, with consequences on parallel computing, convergence diagnostics and performance assessment. The document is written…

There is a lack of simple and scalable algorithms for uncertainty quantification. Bayesian methods quantify uncertainty through posterior and predictive distributions, but it is difficult to rapidly estimate summaries of these…

In statistical analysis, Monte Carlo (MC) stands as a classical numerical integration method. When encountering challenging sample problem, Markov chain Monte Carlo (MCMC) is a commonly employed method. However, the MCMC estimator is biased…

In Monte Carlo integration an accurate and reliable determination of the numerical intregration error is essential. We point out the need for an independent estimate of the error on this error, for which we present an unbiased estimator. In…

Markov chain Monte Carlo is an inherently serial algorithm. Although likelihood calculations for individual steps can sometimes be parallelized, the serial evolution of the process is widely viewed as incompatible with parallelization,…

This work introduces a new method designed for Bayesian deep learning called scalable Bayesian Monte Carlo (SBMC). The method is comprised of a model and an algorithm. The model interpolates between a point estimator and the posterior. The…