Dynamically Weighted Importance Sampling in Monte Carlo Computation

• Published in: Journal of the American Statistical Association Vol. 97; no. 459; pp. 807 - 821
• Main Author: Liang, Faming
• Format: Journal Article
• Language: English
• Published: Alexandria, VA Taylor & Francis 01.09.2002; American Statistical Association
• Subjects: Distribution theory; Driving while intoxicated; Dynamic weighting; Exact sciences and technology; Histograms; Markov chain Monte Carlo; Markov chains; Mathematical extrapolation; Mathematical methods; Mathematical minima; Mathematics; Metropolis-Hastings algorithm; Monte Carlo simulation; Population control; Population dynamics; Population size; Probability and statistics; Sampling theory, sample surveys; Sciences and techniques of general use; Sequential importance sampling; Statistical methods; Statistics; Term weighting; Theory and Methods; Trajectory control; Metropolis algorithm; Monte Carlo method; Statistical distribution; Metropolis Hastings algorithm; Optimization method; Algorithm; Markov chain; Weighting; Sampling theory; Sequential method; Population dynamics; Approximation theory; Sample survey; Importance sampling
• ISSN: 0162-1459; 1537-274X; 1537-274X
• DOI: 10.1198/016214502388618618

This article describes a new Monte Carlo algorithm, dynamically weighted importance sampling (DWIS), for simulation and optimization. In DWIS, the state of the Markov chain is augmented to a population. At each iteration, the population is subject to two move steps, dynamic weighting and population control. These steps ensure that DWIS can move across energy barriers like dynamic weighting, but with the weights well controlled and with a finite expectation. The estimates can converge much faster than they can with dynamic weighting. A generalized theory for importance sampling is introduced to justify the new algorithm. Numerical examples are given to show that dynamically weighted importance sampling can perform significantly better than the Metropolis-Hastings algorithm and dynamic weighting in some situations.