A broad class of implicit or partially implicit time discretizations for the Langevin diffusion are considered and used as proposals for the Metropolis-Hastings algorithm. Ergodic properties of our proposed schemes are studied. We show that introducing implicitness in the discretization leads to a process that often inherits the convergence rate of the continuous time process. These contrast wi...

The Metropolis-Hastings algorithm for estimating a distribution p is based on choosing a candidate Markov chain and then accepting or rejecting moves of the candidate to produce a chain known to have p as the invariant measure. The traditional methods use candidates essentially unconnected to p. We show that the class of candidate distributions, developed in Part I (Stramer and Tweedie 1999), w...

This paper develops a Bayesian computational platform at the interface between posterior sampling and optimization in models whose marginal likelihoods are difficult to evaluate. Inspired by adversarial optimization, namely Generative Adversarial Networks (GAN), we reframe likelihood function estimation problem as classification problem. Pitting Generator, who simulates fake data, against Class...

We study a Monte Carlo algorithm for simulation of probability distributions based on stochastic step functions, and compare to the traditional Metropolis/Hastings method. Unlike the latter, the step function algorithm can produce an uncorrelated Markov chain. We apply this method to the simulation of Levy processes, for which simulation of uncorrelated jumps are essential. We perform numerical...

The Metropolis algorithm [8] is a mainstay of scientific computing. Indeed it appears first on a list of the “Top Ten Algorithms” [12]. It gives a method for sampling from probability distributions on high-dimensional spaces when these distributions are only known up to a normalizing constant. For background and references to extensive applications in physics, chemistry, biology and statistics,...

This paper investigates Bayesian estimation for Gaussian Markov random elds. In particular, a new class of inhomogeneous model is proposed. This inhomogeneous model uses a Markov random eld to describe spatial variation of the smoothing parameter in a second random eld which describes the spatial variation in the observed intensity image. The coupled Markov random elds will be used as prior dis...

The Metropolis–Hastings random walk algorithm remains popular with practitioners due to the wide variety of situations in which it can be successfully applied and extreme ease implemented. Adaptive versions use information from early iterations Markov chain improve efficiency proposal. aim this paper is reduce number needed adapt proposal target, particularly important when likelihood time-cons...

Consider a d-ary rooted tree (d≥ 3) where each edge e is assigned an i.i.d. (bounded) random variable X(e) of negative mean. Assign to each vertex v the sum S(v) of X(e) over all edges connecting v to the root, and assume that the maximum S n of S(v) over all vertices v at distance n from the root tends to infinity (necessarily, linearly) as n tends to infinity. We analyze the Metropolis algori...

A Kernel Adaptive Metropolis-Hastings algorithm is introduced, for the purpose of sampling from a target distribution with strongly nonlinear support. The algorithm embeds the trajectory of the Markov chain into a reproducing kernel Hilbert space (RKHS), such that the feature space covariance of the samples informs the choice of proposal. The procedure is computationally efficient and straightf...