Related papers: Implementing MCMC: Multivariate estimation with co…
This simple note lays out a few observations which are well known in many ways but may not have been said in quite this way before. The basic idea is that when comparing two different Markov chains it is useful to couple them is such a way…
We consider the problem of estimating expectations with respect to a target distribution with an unknown normalizing constant, and where even the unnormalized target needs to be approximated at finite resolution. Under such an assumption,…
In this paper we propose to evaluate and compare Markov chain Monte Carlo (MCMC) methods to estimate the parameters in a generalized extreme value model. We employed the Bayesian approach using traditional Metropolis-Hastings methods,…
A current challenge for many Bayesian analyses is determining when to terminate high-dimensional Markov chain Monte Carlo simulations. To this end, we propose using an automated sequential stopping procedure that terminates the simulation…
Markov Chain Monte Carlo (MCMC) algorithms are commonly used for their versatility in sampling from complicated probability distributions. However, as the dimension of the distribution gets larger, the computational costs for a satisfactory…
Using Markov chain Monte Carlo to sample from posterior distributions was the key innovation which made Bayesian data analysis practical. Notoriously, however, MCMC is hard to tune, hard to diagnose, and hard to parallelize. This…
We study the computational complexity of Markov chain Monte Carlo (MCMC) methods for high-dimensional Bayesian linear regression under sparsity constraints. We first show that a Bayesian approach can achieve variable-selection consistency…
In predictive modeling with simulation or machine learning, it is critical to accurately assess the quality of estimated values through output analysis. In recent decades output analysis has become enriched with methods that quantify the…
Monte Carlo simulations are widely used in many areas including particle accelerators. In this lecture, after a short introduction and reviewing of some statistical backgrounds, we will discuss methods such as direct inversion, rejection…
We propose approaches for testing implementations of Markov Chain Monte Carlo methods as well as of general Monte Carlo methods. Based on statistical hypothesis tests, these approaches can be used in a unit testing framework to, for…
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…
We develop a central limit theorem (CLT) for a non-parametric estimator of the transition matrices in controlled Markov chains (CMCs) with finite state-action spaces. Our results establish precise conditions on the logging policy under…
Markov chain Monte Carlo (MCMC) methods asymptotically sample from complex probability distributions. The pseudo-marginal MCMC framework only requires an unbiased estimator of the unnormalized probability distribution function to construct…
Hamiltonian Monte Carlo (HMC) is a powerful Markov chain Monte Carlo (MCMC) method for performing approximate inference in complex probabilistic models of continuous variables. In common with many MCMC methods, however, the standard HMC…
Markov chain Monte Carlo (MCMC) methods are ubiquitous tools for simulation-based inference in many fields but designing and identifying good MCMC samplers is still an open question. This paper introduces a novel MCMC algorithm, namely,…
Autocorrelations in MCMC chains increase the variance of the estimators they produce. We propose the occlusion process to mitigate this problem. It is a process that sits upon an existing MCMC sampler, and occasionally replaces its samples…
Strong invariance principles in Markov chain Monte Carlo are crucial to theoretically grounded output analysis. Using the wide-sense regenerative nature of the process, we obtain explicit bounds in the strong invariance converging rates for…
This study introduces a computationally efficient algorithm, delayed acceptance Markov chain Monte Carlo (DA-MCMC), designed to improve posterior simulation in quasi-Bayesian inference. Quasi-Bayesian methods, which do not require fully…
Exact approximations of Markov chain Monte Carlo (MCMC) algorithms are a general emerging class of sampling algorithms. One of the main ideas behind exact approximations consists of replacing intractable quantities required to run standard…
This paper presents how to use common random number (CRN) simulation to evaluate Markov chain Monte Carlo (MCMC) convergence to stationarity. We provide an upper bound on the Wasserstein distance of a Markov chain to its stationary…