Monte Carlo integration with Markov chain
نویسنده
چکیده
There are two conceptually distinct tasks in Markov chain Monte Carlo (MCMC): a sampler is designed for simulating a Markov chain and then an estimator is constructed on the Markov chain for computing integrals and expectations. In this article, we aim to address the second task by extending the likelihood approach of Kong et al. for Monte Carlo integration. We consider a general Markov chain scheme and use partial likelihood for estimation. Basically, theMarkov chain scheme is treated as a random design and a stratified estimator is defined for the baseline measure. Further, we propose useful techniques including subsampling, regulation, and amplification for achieving overall computational efficiency. Finally, we introduce approximate variance estimators for the point estimators. The method can yield substantially improved accuracy compared with Chib’s estimator and the crude Monte Carlo estimator, as illustrated with three examples. © 2007 Elsevier B.V. All rights reserved.
منابع مشابه
Coupling control variates for Markov chain Monte Carlo
We show that Markov couplings can be used to improve the accuracy of Markov chain Monte Carlo calculations in some situations where the steady-state probability distribution is not explicitly known. The technique generalizes the notion of control variates from classical Monte Carlo integration. We illustrate it using two models of nonequilibrium transport.
متن کاملMATHEMATICAL ENGINEERING TECHNICAL REPORTS Hamiltonian Monte Carlo with Explicit, Reversible, and Volume-preserving Adaptive Step Size Control
Hamiltonian Monte Carlo is a Markov chain Monte Carlo method that uses Hamiltonian dynamics to efficiently produce distant samples. It employs geometric numerical integration to simulate Hamiltonian dynamics, which is a key of its high performance. We present a Hamiltonian Monte Carlo method with adaptive step size control to further enhance the efficiency. We propose a new explicit, reversible...
متن کاملAn Improved Visible Normal Sampling Routine for the Beckmann Distribution
Recently, Heitz and D’Eon [2014] proposed a method for importance sampling the distribution of visible normals in the context of microfacet BSDF models. One of their sampling routines internally relies on a discontinuous mapping, which can cause problems in conjunction with Quasi Monte Carlo sampling and Markov Chain Monte Carlo integration. In this report, we develop an alternative method that...
متن کامل