A Note on Metropolis - Hastings Kernels for General State
نویسنده
چکیده
The Metropolis-Hastings algorithm is a method of constructing a reversible Markov transition kernel with a speci ed invariant distribution. This note describes necessary and su cient conditions on the candidate generation kernel and the acceptance probability function for the resulting transition kernel and invariant distribution to satisfy the detailed balance conditions. A simple general formulation is used that covers a range of special cases treated separately in the literature. In addition, results on a useful partial ordering of nite state space reversible transition kernels are extended to general state spaces and used to compare the performance of two approaches to using mixtures in Metropolis-Hastings kernels.
منابع مشابه
A Note on Metropolis-Hastings Kernels for General State Spaces
Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your perso...
متن کاملLimit Theorems for Some Adaptive Mcmc Algorithms with Subgeometric Kernels: Part Ii
We prove a central limit theorem for a general class of adaptive Markov Chain Monte Carlo algorithms driven by sub-geometrically ergodic Markov kernels. We discuss in detail the special case of stochastic approximation. We use the result to analyze the asymptotic behavior of an adaptive version of the Metropolis Adjusted Langevin algorithm with a heavy tailed target density.
متن کاملNorges Teknisk-naturvitenskapelige Universitet Control Variates for the Metropolis-hastings Algorithm Control Variates for the Metropolis-hastings Algorithm
We propose new control variates for variance reduction in the Metropolis–Hastings algorithm. We use variates that are functions of both the current state of the Markov chain and the proposed new state. This enable us to specify control variates which have known mean values for general target and proposal distributions. We develop the ideas for both the standard Metropolis–Hastings algorithm and...
متن کاملMarkovian Stochastic Approximation with Expanding Projections
Abstract. Stochastic approximation is a framework unifying many random iterative algorithms occurring in a diverse range of applications. The stability of the process is often difficult to verify in practical applications and the process may even be unstable without additional stabilisation techniques. We study a stochastic approximation procedure with expanding projections similar to Andradótt...
متن کاملExact Transition Probabilities for the Independence Metropolis Sampler
A recent result of Jun Liu's has shown how to compute explicitly the eigen-values and eigenvectors for the Markov chain derived from a special case of the Hastings sampling algorithm, known as the indepdendence Metropolis sampler. In this note, we show how to extend the result to obtain exact n-step transition probabilities for any n. This is done rst for a chain on a nite state space, and then...
متن کامل