TY - JOUR
AU1 - Hastings, W., K.
AB - Downloaded from https://academic.oup.com/biomet/article-abstract/57/1/97/284580 by guest on 14 October 2019 Biometrika (1970), 57, 1, p. 97 97 Printed in Great Britain Monte Carlo sampling methods using Markov chains and their applications B Y W. K. HASTINGS University of Toronto SUMMARY A generalization of the sampling method introduced by Metropolis et al. (1953) is pre- sented 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 applica- tions of the methods to numerical problems arising in statistics, are discussed. 1. INTRODUCTION For numerical problems in a large number of dimensions, Monte Carlo methods are often more efficient than conventional numerical methods. However, implementation of the Monte Carlo methods requires sampling from high dimensional probability distributions and this may be very difficult and expensive in analysis and computer time. General methods for sampling from, or estimating expectations with respect to, such distributions are as follows. (i) If possible, factorize the distribution into the product of one-dimensional conditional distributions from which samples may be obtained. (ii) Use importance sampling, which may also be used for variance reduction. 
TI - Monte Carlo sampling methods using Markov chains and their applications
JF - Biometrika
DO - 10.1093/biomet/57.1.97
DA - 1970-04-01
UR - https://www.deepdyve.com/lp/oxford-university-press/monte-carlo-sampling-methods-using-markov-chains-and-their-604jJ5bY7e
SP - 97
VL - 57
IS - 1
DP - DeepDyve
ER -