Abstract We prove sharp rates of convergence to stationarity for a simple case of the Metropolis algorithm: the placement of a single disc of radius h randomly into the interval [−1 − h, 1 + h], with h > 0 small. We find good approximations for the top eigenvalues and eigenvectors. The analysis gives rigorous proof for the careful numerical work in ([DN04]). The micro-local techniques employed ...

A cluster algorithm is presented for the Z 2 Kalb-Ramond plaquette model in four dimensions which dramatically reduces critical slowing. The critical exponent z is reduced from z > 2 (standard Metropolis algorithm) to z = 0.32 ± 0.06. The Cluster algorithm updates the monopole configuration known to be responsible for the second order phase transition.

We investigate a kinetic Ising model with the Metropolis algorithm on the temporal directed random q-regular graph. We introduce a rewiring time τ as a parameter of the model and show that there is a critical τ = τ ∗ above which the model exhibits continuous order-disorder phase transition and below which the transition is discontinuous. We discuss our findings in a light of the very recent res...

We introduce a new property of Markov chains, called variance bounding. We prove that, for reversible chains at least, variance bounding is weaker than, but closely related to, geometric ergodicity. Furthermore, variance bounding is equivalent to the existence of usual central limit theorems for all L functionals. Also, variance bounding (unlike geometric ergodicity) is preserved under the Pesk...

This paper gives sharp rates of convergence for natural versions of the Metropolis algorithm for sampling from the uniform distribution on a convex polytope. The singular proposal distribution, based on a walk moving locally in one of a fixed, finite set of directions, needs some new tools. We get useful bounds on the spectrum and eigenfunctions using Nash and Weyltype inequalities. The top eig...

This article introduces a generalization of Tanner and Wong’s data augmentation algorithm which can be used when the complete data posterior distribution cannot be directly sampled. The algorithm proposes parameter values based on complete data sampling distributions of convenient frequentist estimators which ignore some information in the complete data likelihood. The proposals are filtered us...

Seismic inversion is one of the important methods to realize reservoir prediction in oil and gas field exploration. The seismic stochastic based on Metropolis-Hastings algorithm makes full use well logging data improves vertical resolution results. However, conventional has slow convergence speed poor stability. In this paper, an elastic impedance method optimized established by combining quant...

This note describes a selection procedure for genetic algorithms called Boltzmann tournament selection. As simulated annealing evolves a Boltzmann distribution in time using the Metropolis algorithm or a logistic acceptance mechanism, Boltzmann tournament selection evolves a Boltzmann distribution across a population and time using pairwise probabilistic acceptance and anti-acceptance mechanism...

The Metropolis-Hastings (MH) algorithm is a way to sample a provided target distribution π(x). It works by repeatedly sampling a separate proposal distribution T (x, x) to generate a random walk {x(t)}. We consider a modification of the MH algorithm in which T is dynamically updated during the walk. The update at time t uses the {x(t < t)} to estimate the product distribution that has the least...

Use of auxiliary variables for generating proposal variables within a MetropolisHastings setting has been suggested in many different settings. This has in particular been of interest for simulation from complex distributions such as multimodal distributions or in transdimensional approaches. For many of these approaches, the acceptance probabilities that are used turn up somewhat magic and dif...