Abstract

this paper, a special Metropolis-Hastings type algorithm, Metropolized independent sampling, proposed firstly in Hastings (1970), is studied in full detail. The eigenvalues and eigenvectors of the corresponding Markov chain, as well as a sharp bound for the total variation distance between the n-th updated distribution and the target distribution, are provided. Furthermore, the relationship between this scheme, rejection sampling, and importance sampling are studied with emphasizes on their relative efficiencies. It is shown that Metropolized independent sampling is superior to rejection sampling in two aspects: asymptotic efficiency and ease of computation. Key Words: Coupling, Delta method, Eigen analysis, Importance ratio. 1 1 Introduction

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