We connect known results about diffusion limits of Markov chain Monte Carlo (MCMC) algorithms to the Computer Science notion of algorithm complexity. Our main result states that any diffusion limit of a Markov process implies a corresponding complexity bound (in an appropriate metric). We then combine this result with previously-known MCMC diffusion limit results to prove that under appropriate...

Application of the Metropolis algorithm for forest harvest scheduling is extended by automating the relative weighting of objective function components. Previous applications of the Metropolis algorithm require the user to specify these weights, which demands substantial trial and error in practice. This modification allows for general incorporation of objective function components that are eit...

This report provides a progress update on our microarchitectural modeling of the XScale and Strongarm processors using a process-networks model of computation within the Metropolis design framework. This work provides rapid and accurate specification of microarchitectural performance models for CPU’s. In particular, we present the two major improvements from our previous report. First, we moved...

In this paper we develop tools for analyzing the rate at which a reversible Markov chain converges to stationarity. Our techniques are useful when the Markov chain can be decomposed into pieces which are themselves easier to analyze. The main theorems relate the spectral gap of the original Markov chains to the spectral gap of the pieces. In the first case the pieces are restrictions of the Mar...

We study the slice sampler, a method of constructing a reversible Markov chain with a speciied invariant distribution. Given an independence Metropolis-Hastings algorithm it is always possible to construct a slice sampler that dominates it in the Peskun sense. This means that the resulting Markov chain produces estimates with a smaller asymptotic variance. Furthermore the slice sampler has a sm...

We propose a novel adaptive MCMC algorithm named AMOR (Adaptive Metropolis with Online Relabeling) for efficiently simulating from permutation-invariant targets occurring in, for example, Bayesian analysis of mixture models. An important feature of the algorithm is to tie the adaptation of the proposal distribution to the choice of a particular restriction of the target to a domain where label ...

The classical Metropolis sampling method is a cornerstone of many statistical modeling applications that range from physics, chemistry, and biology to economics. This method is particularly suitable for sampling the thermal distributions of classical systems. The challenge of extending this method to the simulation of arbitrary quantum systems is that, in general, eigenstates of quantum Hamilto...

Stormwater models underpin decision-making processes in stormwater management. Runoff generation and flow routing models are now well developed and widely adopted. However, stormwater quality models are less well developed. Model calibration and sensitivity analysis are crucial in order to estimate realistic stormwater pollution concentrations. The Metropolis algorithm (Metropolis et al., 1953)...

This article provides a brief review of recent developments in Markov chain Monte Carlo methodology. The methods discussed include the standard Metropolis-Hastings algorithm, the Gibbs sampler, and various special cases of interest to practitioners. It also devotes a section on strategies for improving mixing rate of MCMC samplers, e.g., simulated tempering, parallel tempering, parameter expans...

We compare convergence rates of Metropolis–Hastings chains to multimodal target distributions when the proposal distributions can be of “local” and “small world” type. In particular, we show that by adding occasional long-range jumps to a given local proposal distribution, one can turn a chain that is “slowly mixing” (in the complexity of the problem) into a chain that is “rapidly mixing.” To d...