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March 2014 Zero Variance Differential Geometric Markov Chain Monte Carlo Algorithms
Theodore Papamarkou, Antonietta Mira, Mark Girolami
Bayesian Anal. 9(1): 97-128 (March 2014). DOI: 10.1214/13-BA848


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.


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Theodore Papamarkou. Antonietta Mira. Mark Girolami. "Zero Variance Differential Geometric Markov Chain Monte Carlo Algorithms." Bayesian Anal. 9 (1) 97 - 128, March 2014.


Published: March 2014
First available in Project Euclid: 24 February 2014

zbMATH: 1327.60140
MathSciNet: MR3188301
Digital Object Identifier: 10.1214/13-BA848

Keywords: control variates , Hamiltonian Monte Carlo , Metropolis adjusted Langevin algorithms , Metropolis-Hastings

Rights: Copyright © 2014 International Society for Bayesian Analysis

Vol.9 • No. 1 • March 2014
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