Optimal Scaling for Partially Updating Mcmc Algorithms
نویسندگان
چکیده
In this paper we shall consider optimal scaling problems for highdimensional Metropolis–Hastings algorithms where updates can be chosen to be lower dimensional than the target density itself. We find that the optimal scaling rule for the Metropolis algorithm, which tunes the overall algorithm acceptance rate to be 0.234, holds for the so-called Metropolis-within-Gibbs algorithm as well. Furthermore, the optimal efficiency obtainable is independent of the dimensionality of the update rule. This has important implications for the MCMC practitioner since high-dimensional updates are generally computationally more demanding, so that lower-dimensional updates are therefore to be preferred. Similar results with rather different conclusions are given for so-called Langevin updates. In this case, it is found that high-dimensional updates are frequently most efficient, even taking into account computing costs.
منابع مشابه
Weak Convergence and Optimal Proposals for Monte Carlo Algorithms
Metropolis-Hastings Markov chain Monte Carlo (MCMC) algorithms and other popular MCMC algorithms induce a Markov chain which has the target distribution as its stationary distribution. Optimal scaling refers to the need to tune the parameters of the proposal kernel in order to ensure the Markov chain obtained from the algorithm converges as fast as possible to stationarity. Theoretical results ...
متن کاملOn Block Updating in Markov Random Field Models for Disease Mapping
Gaussian Markov random field (GMRF) models are commonly used to model spatial correlation in disease mapping applications. For Bayesian inference by MCMC, so far mainly single-site updating algorithms have been considered. However, convergence and mixing properties of such algorithms can be extremely poor due to strong dependencies of parameters in the posterior distribution. In this paper, we ...
متن کاملOptimal Proposal Distributions and Adaptive MCMC by Jeffrey
We review recent work concerning optimal proposal scalings for Metropolis-Hastings MCMC algorithms, and adaptive MCMC algorithms for trying to improve the algorithm on the fly.
متن کاملOptimal Proposal Distributions and Adaptive MCMC
We review recent work concerning optimal proposal scalings for Metropolis-Hastings MCMC algorithms, and adaptive MCMC algorithms for trying to improve the algorithm on the fly.
متن کاملMCMC algorithms for Subset Simulation
Subset Simulation is an adaptive simulation method that efficiently solves structural reliability problems with many random variables. The method requires sampling from conditional distributions, which is achieved through Markov Chain Monte Carlo (MCMC) algorithms. This paper discusses different MCMC algorithms proposed for Subset Simulation and introduces a novel approach for MCMC sampling in ...
متن کامل