Norges Teknisk-naturvitenskapelige Universitet Control Variates for the Metropolis-hastings Algorithm Control Variates for the Metropolis-hastings Algorithm
نویسندگان
چکیده
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 the generalized reversible jump version. We present simulation results for four simulation examples. The variance reduction varies depending on the target distribution and proposal mechanisms used, the typical relative variance reduction is between 15% and 35%.
منابع مشابه
Norges Teknisk-naturvitenskapelige Universitet Directional Metropolis–hastings Updates for Posteriors with Nonlinear Likelihoods Directional Metropolis–hastings Updates for Posteriors with Nonlinear Likelihoods
In this paper we consider spatial problems modeled by a Gaussian random field prior density and a nonlinear likelihood function linking the hidden variables to the observed data. We define a directional block Metropolis–Hastings algorithm to explore the posterior density. The method is applied to seismic data from the North Sea. Based on our results we believe it is important to assess the actu...
متن کاملDoes Waste Recycling Really Improve the Multi-proposal Metropolis–hastings Algorithm? an Analysis Based on Control Variates
The waste-recycling Monte Carlo (WRMC) algorithm introduced by physicists is a modification of the (multi-proposal) Metropolis–Hastings algorithm, which makes use of all the proposals in the empirical mean, whereas the standard (multi-proposal) Metropolis–Hastings algorithm uses only the accepted proposals. In this paper we extend the WRMC algorithm to a general control variate technique and ex...
متن کاملOn the Poisson Equation for Metropolis-hastings Chains
This paper defines an approximation scheme for a solution of the Poisson equation of a geometrically ergodic Metropolis-Hastings chain Φ. The scheme is based on the idea of weak approximation and gives rise to a natural sequence of control variates for the ergodic average Sk(F ) = (1/k) ∑k i=1 F (Φi), where F is the force function in the Poisson equation. The main results show that the sequence...
متن کاملDoes Waste-recycling Really Improve the Multi-proposal Metropolis-hastings Monte Carlo Algorithm?
The waste-recycling Monte Carlo (WR) algorithm introduced by physicists is a modification of the (multi-proposal) Metropolis-Hastings algorithm, which makes use of all the proposals in the empirical mean, whereas the standard (multi-proposal) Metropolis-Hastings algorithm only uses the accepted proposals. In this paper, we extend the WR algorithm into a general control variate technique and exh...
متن کاملDoes Waste-recycling Really Improve the Multi-proposal Metropolis-hastings Monte Carlo Algorithm?
The waste-recycling Monte Carlo (WR) algorithm introduced by physicists is a modification of the (multi-proposal) Metropolis-Hastings algorithm, which makes use of all the proposals in the empirical mean, whereas the standard (multi-proposal) MetropolisHastings algorithm only uses the accepted proposals. In this paper, we extend the WR algorithm into a general control variate technique and exhi...
متن کامل