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February 2009 Adaptive independent Metropolis–Hastings
Lars Holden, Ragnar Hauge, Marit Holden
Ann. Appl. Probab. 19(1): 395-413 (February 2009). DOI: 10.1214/08-AAP545

Abstract

We propose an adaptive independent Metropolis–Hastings algorithm with the ability to learn from all previous proposals in the chain except the current location. It is an extension of the independent Metropolis–Hastings algorithm. Convergence is proved provided a strong Doeblin condition is satisfied, which essentially requires that all the proposal functions have uniformly heavier tails than the stationary distribution. The proof also holds if proposals depending on the current state are used intermittently, provided the information from these iterations is not used for adaption. The algorithm gives samples from the exact distribution within a finite number of iterations with probability arbitrarily close to 1. The algorithm is particularly useful when a large number of samples from the same distribution is necessary, like in Bayesian estimation, and in CPU intensive applications like, for example, in inverse problems and optimization.

Citation

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Lars Holden. Ragnar Hauge. Marit Holden. "Adaptive independent Metropolis–Hastings." Ann. Appl. Probab. 19 (1) 395 - 413, February 2009. https://doi.org/10.1214/08-AAP545

Information

Published: February 2009
First available in Project Euclid: 20 February 2009

zbMATH: 1192.65009
MathSciNet: MR2498682
Digital Object Identifier: 10.1214/08-AAP545

Subjects:
Primary: 65C05
Secondary: 65C40

Keywords: Adaption , Inverse problems , Markov chain Monte Carlo , Metropolis–Hastings

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.19 • No. 1 • February 2009
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