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An Adaptive Metropolis algorithm
 Bernoulli
, 1998
"... A proper choice of a proposal distribution for MCMC methods, e.g. for the MetropolisHastings algorithm, is well known to be a crucial factor for the convergence of the algorithm. In this paper we introduce an adaptive Metropolis Algorithm (AM), where the Gaussian proposal distribution is updated al ..."
Abstract

Cited by 216 (8 self)
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A proper choice of a proposal distribution for MCMC methods, e.g. for the MetropolisHastings algorithm, is well known to be a crucial factor for the convergence of the algorithm. In this paper we introduce an adaptive Metropolis Algorithm (AM), where the Gaussian proposal distribution is updated
Metropolis algorithm
"... We want to infer about θ based on the sample Y = (Y1,...,Yn) Bayesian models assume a prior θ ∼ p(θ) where p(θ) is a valid density Inference about θ given the sample Y = (Y1,...,Yn) is based on the posterior distribution p(θ Y) Markov Chain Monte Carlo: Samples are generated from p(θ Y) Note that ..."
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We want to infer about θ based on the sample Y = (Y1,...,Yn) Bayesian models assume a prior θ ∼ p(θ) where p(θ) is a valid density Inference about θ given the sample Y = (Y1,...,Yn) is based on the posterior distribution p(θ Y) Markov Chain Monte Carlo: Samples are generated from p(θ Y) Note that p(θ Y) = p(Y, θ)/p(Y) = p(Y  θ)p(θ)/p(Y) p(Y) = p(Y  θ)p(θ)dθ is the normalizing constant free of θ
Rates of convergence of the Hastings and Metropolis algorithms
 ANNALS OF STATISTICS
, 1996
"... We apply recent results in Markov chain theory to Hastings and Metropolis algorithms with either independent or symmetric candidate distributions, and provide necessary and sufficient conditions for the algorithms to converge at a geometric rate to a prescribed distribution ß. In the independence ca ..."
Abstract

Cited by 215 (17 self)
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We apply recent results in Markov chain theory to Hastings and Metropolis algorithms with either independent or symmetric candidate distributions, and provide necessary and sufficient conditions for the algorithms to converge at a geometric rate to a prescribed distribution ß. In the independence
Geometric ergodicity of Metropolis algorithms
 STOCHASTIC PROCESSES AND THEIR APPLICATIONS
, 1998
"... In this paper we derive conditions for geometric ergodicity of the random walkbased Metropolis algorithm on R k . We show that at least exponentially light tails of the target density is a necessity. This extends the onedimensional result of (Mengersen and Tweedie, 1996). For subexponential targe ..."
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Cited by 85 (2 self)
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In this paper we derive conditions for geometric ergodicity of the random walkbased Metropolis algorithm on R k . We show that at least exponentially light tails of the target density is a necessity. This extends the onedimensional result of (Mengersen and Tweedie, 1996). For sub
Geometric analysis for the Metropolis algorithm on . . .
"... This paper gives geometric tools: comparison, Nash and Sobolev inequalities for pieces of the relevent Markov operators, that give useful bounds on rates of convergence for the Metropolis algorithm. As an example, we treat the random placement of N hard discs in the unit square, the original applica ..."
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Cited by 21 (11 self)
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This paper gives geometric tools: comparison, Nash and Sobolev inequalities for pieces of the relevent Markov operators, that give useful bounds on rates of convergence for the Metropolis algorithm. As an example, we treat the random placement of N hard discs in the unit square, the original
Metropolis algorithm on convex polytops
 Mathematische Zeitschrift
"... This paper gives sharp rates of convergence for natural versions of the Metropolis algorithm for sampling from the uniform distribution on a convex polytope. The singular proposal distribution, based on a walk moving locally in one of a fixed, finite set of directions, needs some new tools. We get ..."
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Cited by 2 (1 self)
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This paper gives sharp rates of convergence for natural versions of the Metropolis algorithm for sampling from the uniform distribution on a convex polytope. The singular proposal distribution, based on a walk moving locally in one of a fixed, finite set of directions, needs some new tools. We get
Exploring an Adaptive Metropolis Algorithm
, 2010
"... While adaptive methods for MCMC are under active development, their utility has been underrecognized. We briefly review some theoretical results relevant to adaptive MCMC. We then suggest a very simple and effective algorithm to adapt proposal densities for random walk Metropolis and Metropolis adj ..."
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Cited by 4 (0 self)
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While adaptive methods for MCMC are under active development, their utility has been underrecognized. We briefly review some theoretical results relevant to adaptive MCMC. We then suggest a very simple and effective algorithm to adapt proposal densities for random walk Metropolis and Metropolis
Weak Convergence And Optimal Scaling Of Random Walk Metropolis Algorithms
, 1994
"... This paper considers the problem of scaling the proposal distribution of a multidimensional random walk Metropolis algorithm, in order to maximize the efficiency of the algorithm. The main result is a weak convergence result as the dimension of a sequence of target densities, n, converges to infinit ..."
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Cited by 282 (35 self)
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This paper considers the problem of scaling the proposal distribution of a multidimensional random walk Metropolis algorithm, in order to maximize the efficiency of the algorithm. The main result is a weak convergence result as the dimension of a sequence of target densities, n, converges
Results 1  10
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30,132