Abstract
An Adaptive Importance Sampling (AIS) scheme is introduced to compute integrals of the form [Formula Omitted] as a mechanical, yet flexible, way of dealing with the selection of parameters of the importance function. AIS starts with a rough estimate for the parameters λ of the importance function [Formula Omitted], and runs importance sampling in an iterative way to continually update λ using only linear accumulation. Consistency of AIS is established. The efficiency of the algorithm is studied in three examples and found to be substantially superior to ordinary importance sampling.
| Original language | English |
|---|---|
| Pages (from-to) | 143-168 |
| Number of pages | 26 |
| Journal | Journal of Statistical Computation and Simulation |
| Volume | 41 |
| Issue number | 3-4 |
| DOIs | |
| State | Published - 1 Jul 1992 |
Bibliographical note
Funding Information:"Research was supported by the National Science Foundation, grants DMS-8702620 and DMS-8717799, and by a David Ross Fellowship from Purdue University, as part of the first author's Ph.D. thesis. Parts of the work were also done while the authors were visiting at Duke University. The authors thank Arup Bose for his help with the convergence proofs.
Keywords
- Monte Carlo integration
- adaptive importance sampling
- approximate normality
- basic importance sampling
- importance function
- linear accumulation
- martingale limit theorem