DeepAI AI Chat
Log In Sign Up

Quasi Markov Chain Monte Carlo Methods

06/29/2018
by   Tobias Schwedes, et al.
0

Quasi-Monte Carlo (QMC) methods for estimating integrals are attractive since the resulting estimators converge at a faster rate than pseudo-random Monte Carlo. However, they can be difficult to set up on arbitrary posterior densities within the Bayesian framework, in particular for inverse problems. We introduce a general parallel Markov chain Monte Carlo (MCMC) framework, for which we prove a law of large numbers and a central limit theorem. We further extend this approach to the use of adaptive kernels and state conditions, under which ergodicity holds. As a further extension, an importance sampling estimator is derived, for which asymptotic unbiasedness is proven. We consider the use of completely uniformly distributed (CUD) numbers and non-reversible transitions within the above stated methods, which leads to a general parallel quasi-MCMC (QMCMC) methodology. We prove consistency of the resulting estimators and demonstrate numerically that this approach scales close to n^-1 as we increase parallelisation, instead of the usual n^-1/2 that is typical of standard MCMC algorithms. In practical statistical models we observe up to 2 orders of magnitude improvement compared with pseudo-random methods.

READ FULL TEXT

page 1

page 2

page 3

page 4

04/11/2019

Markov chain Monte Carlo importance samplers for Bayesian models with intractable likelihoods

We consider the efficient use of an approximation within Markov chain Mo...
01/18/2023

An MCMC Approach to Classical Estimation

This paper studies computationally and theoretically attractive estimato...
02/20/2020

A table of short-period Tausworthe generators for Markov chain quasi-Monte Carlo

We consider the problem of estimating expectations by using Markov chain...
06/01/2021

Efficient adaptive MCMC implementation for Pseudo-Bayesian quantum tomography

We revisit the Pseudo-Bayesian approach to the problem of estimating den...
01/28/2018

Air Markov Chain Monte Carlo

We introduce a class of Adapted Increasingly Rarely Markov Chain Monte C...
04/22/2017

Reversible Jump Metropolis Light Transport using Inverse Mappings

We study Markov Chain Monte Carlo (MCMC) methods operating in primary sa...