Probabilistic regressor chains with Monte Carlo methods

Monte Carlo without Chains

A sampling method for spin systems is presented. The spin lattice is written as the union of a nested sequence of sublattices, all but the last with conditionally independent spins, which are sampled in succession using their marginals. The marginals are computed concurrently by a fast algorithm; errors in the evaluation of the marginals are offset by weights. There are no Markov chains and eac...

Monte Carlo sampling methods using Markov chains and their applications

A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising ...

Monte Carlo Sampling Methods Using Markov Chains and Their Applications

Monte Carlo and quasi-Monte Carlo methods

Monte Carlo is one of the most versatile and widely used numerical methods. Its convergence rate, O(N~^), is independent of dimension, which shows Monte Carlo to be very robust but also slow. This article presents an introduction to Monte Carlo methods for integration problems, including convergence theory, sampling methods and variance reduction techniques. Accelerated convergence for Monte Ca...

Ordering Monte Carlo Markov Chains

Markov chains having the same stationary distribution can be partially ordered by performance in the central limit theorem. We say that one chain is at least as good as another in the e ciency partial ordering if the variance in the central limit theorem is at least as small for every L( ) functional of the chain. Peskun partial ordering implies e ciency partial ordering [25, 30]. Here we show ...