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Improving Convergence of the Hastings–Metropolis Algorithm with an Adaptive Proposal
Author(s) -
CHAUVEAU DIDIER,
VANDEKERKHOVE PIERRE
Publication year - 2002
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00064
Subject(s) - metropolis–hastings algorithm , mathematics , markov chain monte carlo , algorithm , markov chain , convergence (economics) , density estimation , distribution (mathematics) , sampling (signal processing) , parametric statistics , extension (predicate logic) , statistics , computer science , monte carlo method , mathematical analysis , economics , economic growth , filter (signal processing) , estimator , computer vision , programming language
The Hastings–Metropolis algorithm is a general MCMC method for sampling from a density known up to a constant. Geometric convergence of this algorithm has been proved under conditions relative to the instrumental (or proposal) distribution. We present an inhomogeneous Hastings–Metropolis algorithm for which the proposal density approximates the target density, as the number of iterations increases. The proposal density at the n th step is a non‐parametric estimate of the density of the algorithm, and uses an increasing number of i.i.d. copies of the Markov chain. The resulting algorithm converges (in n ) geometrically faster than a Hastings–Metropolis algorithm with any fixed proposal distribution. The case of a strictly positive density with compact support is presented first, then an extension to more general densities is given. We conclude by proposing a practical way of implementation for the algorithm, and illustrate it over simulated examples.