TY - JOUR

T1 - Optimal metropolis algorithms for product measures on the vertices of a hypercube.

AU - Roberts, G. O.

PY - 1997

Y1 - 1997

N2 - Optimal scaling problems for high dimensional Metropolis-Hastings algorithms can often be solved by means of diffusion approximation results. These solutions are particularly appealing since they can often be characterised in terms of a simple, observable property of the Markov chain sample path, namely the overall proportion of accepted iterations for the chain. For discrete state space problems, analogous scaling problems can be defined, though due to discrete effects, a simple characterisation of the asymptotically optimal solution is not available. This paper considers the simplest possible (and most discrete) example of such a problem, demonstrating that, at least for sufficiently 'smooth' distributions in high dimensional problems,the Metropolis algorithm behaves similarly to its counterpart on the continuous state space

AB - Optimal scaling problems for high dimensional Metropolis-Hastings algorithms can often be solved by means of diffusion approximation results. These solutions are particularly appealing since they can often be characterised in terms of a simple, observable property of the Markov chain sample path, namely the overall proportion of accepted iterations for the chain. For discrete state space problems, analogous scaling problems can be defined, though due to discrete effects, a simple characterisation of the asymptotically optimal solution is not available. This paper considers the simplest possible (and most discrete) example of such a problem, demonstrating that, at least for sufficiently 'smooth' distributions in high dimensional problems,the Metropolis algorithm behaves similarly to its counterpart on the continuous state space

KW - Metropolis-Hastings algorithm

KW - scaling problem

KW - weak convergence

KW - Mathematics Subject Classification 1991

KW - Primary

KW - 60F05

KW - Secondary

KW - 65U05

U2 - 10.1080/17442509808834136

DO - 10.1080/17442509808834136

M3 - Journal article

VL - 62

SP - 275

EP - 284

JO - Stochastics

JF - Stochastics

SN - 1744-2516

IS - 3 & 4

ER -