Bayesian Analysis

Zero Variance Differential Geometric Markov Chain Monte Carlo Algorithms

Theodore Papamarkou, Antonietta Mira, and Mark Girolami

Full-text: Open access

Abstract

Differential geometric Markov Chain Monte Carlo (MCMC) strategies exploit the geometry of the target to achieve convergence in fewer MCMC iterations at the cost of increased computing time for each of the iterations. Such computational complexity is regarded as a potential shortcoming of geometric MCMC in practice. This paper suggests that part of the additional computing required by Hamiltonian Monte Carlo and Metropolis adjusted Langevin algorithms produces elements that allow concurrent implementation of the zero variance reduction technique for MCMC estimation. Therefore, zero variance geometric MCMC emerges as an inherently unified sampling scheme, in the sense that variance reduction and geometric exploitation of the parameter space can be performed simultaneously without exceeding the computational requirements posed by the geometric MCMC scheme alone. A MATLAB package is provided, which implements a generic code framework of the combined methodology for a range of models.

Article information

Source
Bayesian Anal., Volume 9, Number 1 (2014), 97-128.

Dates
First available in Project Euclid: 24 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.ba/1393251772

Digital Object Identifier
doi:10.1214/13-BA848

Mathematical Reviews number (MathSciNet)
MR3188301

Zentralblatt MATH identifier
1327.60140

Keywords
Metropolis-Hastings Hamiltonian Monte Carlo Metropolis adjusted Langevin algorithms Control variates

Citation

Papamarkou, Theodore; Mira, Antonietta; Girolami, Mark. Zero Variance Differential Geometric Markov Chain Monte Carlo Algorithms. Bayesian Anal. 9 (2014), no. 1, 97--128. doi:10.1214/13-BA848. https://projecteuclid.org/euclid.ba/1393251772


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