The Annals of Applied Probability

Adaptive independent Metropolis–Hastings

Lars Holden, Ragnar Hauge, and Marit Holden

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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.

Article information

Ann. Appl. Probab., Volume 19, Number 1 (2009), 395-413.

First available in Project Euclid: 20 February 2009

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Zentralblatt MATH identifier

Primary: 65C05: Monte Carlo methods
Secondary: 65C40: Computational Markov chains

Adaption Metropolis–Hastings Markov chain Monte Carlo inverse problems


Holden, Lars; Hauge, Ragnar; Holden, Marit. Adaptive independent Metropolis–Hastings. Ann. Appl. Probab. 19 (2009), no. 1, 395--413. doi:10.1214/08-AAP545.

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