I show how one can modify the random-walk Metropolis MCMC method in such a way that a sequence of modified Metropolis updates takes little computation time when the rejection rate is outside a desired interval. This allows one to effectively adapt the scale of the Metropolis proposal distribution, by performing several such “short-cut” Metropolis sequences with varying proposal stepsizes. Unlik...

The waste-recycling Monte Carlo (WR) algorithm, introduced by Frenkel, is a modification of the Metropolis-Hastings algorithm, which makes use of all the proposals, whereas the standard Metropolis-Hastings algorithm only uses the accepted proposals. We prove the convergence of the WR algorithm and its asymptotic normality. We give an example which shows that in general the WR algorithm is not a...

Metropolis is an integrated development environment for system-level design that embodies the concepts of the platform-based design methodology. Metropolis is based on a Metamodel with formal semantics and allows not only design capture, but also formal analysis, synthesis and simulation. After reviewing the basic concepts behind Metropolis, we will describe a realistic use-case scenario that s...

This paper presents a method for adaptation in Metropolis-Hastings algorithms. A product of a proposal density and K copies of the target density is used to define a joint density which is sampled by a Gibbs sampler including a Metropolis step. This provides a framework for adaptation since the current value of all K copies of the target distribution can be used in the proposal distribution. Th...

In an attempt to improve on the Metropolis algorithm, various MCMC methods involving pools of proposals, such as the multiple-try Metropolis and delayed rejection strategies, have been proposed. These methods generate several candidates in a single iteration; accordingly they are computationally more intensive than the Metropolis algorithm. In this paper, we consider three samplers with pools o...

It is illustrated for 4D SU(2) lattice gauge theory that sampling with a biased Metropolis scheme is essentially equivalent to using the heatbath algorithm. Only, the biased Metropolis method can also be applied when an efficient heatbath algorithm does not exist. Other cases for which the use of the biased Metropolis-heatbath algorithm is beneficial are briefly summarized.

We investigate the use of adaptive MCMC algorithms to automatically tune the Markov chain parameters during a run. Examples include the Adaptive Metropolis (AM) multivariate algorithm of Haario et al. (2001), Metropolis-within-Gibbs algorithms for non-conjugate hierarchical models, regionally adjusted Metropolis algorithms, and logarithmic scalings. Computer simulations indicate that the algori...

We investigate the use of adaptive MCMC algorithms to automatically tune the Markov chain parameters during a run. Examples include the Adaptive Metropolis (AM) multivariate algorithm of Haario et al. (2001), Metropolis-within-Gibbs algorithms for non-conjugate hierarchical models, regionally adjusted Metropolis algorithms, and logarithmic scalings. Computer simulations indicate that the algori...

The Multiple-Try Metropolis is a recent extension of the Metropolis algorithm in which the next state of the chain is selected among a set of proposals. We propose a modification of the Multiple-Try Metropolis algorithm which allows for the use of correlated proposals, particularly antithetic and stratified proposals. The method is particularly useful for random walk Metropolis in high dimensio...

We investigate the use of adaptive MCMC algorithms to automatically tune the Markov chain parameters during a run. Examples include the Adaptive Metropolis (AM) multivariate algorithm of Haario et al. (2001), Metropolis-within-Gibbs algorithms for non-conjugate hierarchical models, regionally adjusted Metropolis algorithms, and logarithmic scalings. Computer simulations indicate that the algori...