Related papers: Hypothesis testing for Markov chain Monte Carlo
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…
We consider quantile estimation using Markov chain Monte Carlo and establish conditions under which the sampling distribution of the Monte Carlo error is approximately Normal. Further, we investigate techniques to estimate the associated…
The aim of this paper is to propose a methodology for testing general hypothesis in a Markovian setting with random sampling. A discrete Markov chain X is observed at random time intervals $\tau$ k, assumed to be iid with unknown…
Bayesian analysis often concerns an evaluation of models with different dimensionality as is necessary in, for example, model selection or mixture models. To facilitate this evaluation, transdimensional Markov chain Monte Carlo (MCMC)…
Markov chains can be used to generate samples whose distribution approximates a given target distribution. The quality of the samples of such Markov chains can be measured by the discrepancy between the empirical distribution of the samples…
Statistical models can involve implicitly defined quantities, such as solutions to nonlinear ordinary differential equations (ODEs), that unavoidably need to be numerically approximated in order to evaluate the model. The approximation…
Markov chain models are used in various fields, such behavioral sciences or econometrics. Although the goodness of fit of the model is usually assessed by large sample approximation, it is desirable to use conditional tests if the sample…
The steadily increasing size of scientific Monte Carlo simulations and the desire for robust, correct, and reproducible results necessitates rigorous testing procedures for scientific simulations in order to detect numerical problems and…
We propose a Monte Carlo algorithm to sample from high dimensional probability distributions that combines Markov chain Monte Carlo and importance sampling. We provide a careful theoretical analysis, including guarantees on robustness to…
Markov chain Monte Carlo methods are often deemed too computationally intensive to be of any practical use for big data applications, and in particular for inference on datasets containing a large number $n$ of individual data points, also…
Bayesian hierarchical modeling is a popular approach to capturing unobserved heterogeneity across individual units. However, standard estimation methods such as Markov chain Monte Carlo (MCMC) can be impracticable for modeling outcomes from…
We devise a Monte Carlo based method for detecting whether a non-negative Markov chain is stable for a given set of parameter values. More precisely, for a given subset of the parameter space, we develop an algorithm that is capable of…
Markov chain Monte Carlo is a method of producing a correlated sample in order to estimate features of a target distribution via ergodic averages. A fundamental question is when should sampling stop? That is, when are the ergodic averages…
Calculating a Monte Carlo standard error (MCSE) is an important step in the statistical analysis of the simulation output obtained from a Markov chain Monte Carlo experiment. An MCSE is usually based on an estimate of the variance of the…
Monte Carlo (MC) sampling methods are widely applied in Bayesian inference, system simulation and optimization problems. The Markov Chain Monte Carlo (MCMC) algorithms are a well-known class of MC methods which generate a Markov chain with…
In recent times empirical likelihood has been widely applied under Bayesian framework. Markov chain Monte Carlo (MCMC) methods are frequently employed to sample from the posterior distribution of the parameters of interest. However,…
Monte Carlo experiments produce samples in order to estimate features of a given distribution. However, simultaneous estimation of means and quantiles has received little attention, despite being common practice. In this setting we…
We consider the efficient use of an approximation within Markov chain Monte Carlo (MCMC), with subsequent importance sampling (IS) correction of the Markov chain inexact output, leading to asymptotically exact inference. We detail…
Particle Markov Chain Monte Carlo methods are used to carry out inference in non-linear and non-Gaussian state space models, where the posterior density of the states is approximated using particles. Current approaches usually perform…
Consider testing multiple hypotheses using tests that can only be evaluated by simulation, such as permutation tests or bootstrap tests. This article introduces MMCTest, a sequential algorithm which gives, with arbitrarily high probability,…