Exponential convergence of adaptive importance sampling for Markov chains

Journal of Applied Probability

Volumn 37, Issue 2, 2000, Pages 342-358

  Baggerly, Keith ^a,d   Cox, Dennis ^b   Picard, Rick ^c  

^a RICE UNIVERSITY   (United States)

^b NATIONAL CENTER FOR ATMOSPHERIC RESEARCH   (United States)

^c LOS ALAMOS NATIONAL LABORATORY   (United States)

^d Rice University   (United States)

Author keywords

Adaptive procedures; Biased random walks; Learning algorithms; Monte Carlo simulation; Particle transport; Zero variance solution

Indexed keywords

EID: 0034339278     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1239/jap/1014842541     Document Type: Article

References (13)

1. APOSTOL, T. A. (1957). MathematicalAnalysis. Addison-Wesley, Reading, MA.
2. BAGGERLY, K., Cox, D. AND Picard, R. (1998). Adaptive importance sampling for random walks on continuous state spaces. Los Alamos National Laboratory Tech. Rep. LA-UR-98-1214. Available at http://www-xdiv.lanl.gov/XTM/projects/mc21/docs/aspublication25.
3. BOOTH, T. E. (1985). Exponential convergencefor Monte Carlo particle transport? Trans. Amer. Nucl. Soc. 50, 267-268.
4. BOOTH, T. E. (1989). Zero-variance solutions for linear Monte Carlo. Nucl. Sci. Eng. 102,332-340.
5. BOOTH, T. E. (1997). Exponential convergence on a continuous Monte Carlo transport problem. Nucl. Sci. Eng. 127, 338-345.
6. BREIMAN, L. (1968). Probability. Addison-Wesley, Reading, MA.
7. GLASSERMAN, P. (1993). Stochastic monotonicityand conditionalMonte Carloforlikelihoodratios. Adv.Appl. Prob. 25, 103-115.
8. KOLLMAN, C. (1993). Rare event simulation in radiation transport. Unpublished Ph.D. thesis, Stanford University.
9. KOLLMAN, C., BAGGERLY, K., Cox, D. and Picard, R. (1999). Adaptive importance sampling on discrete Markovchains. Ann.Appl. Prob. 9, 391-412.
10. LUX, I. AND KOBLINGER, L. (1991). Monte Carlo Particle Transport Methods: Neutron and Photon Calculations. CRC Press, Boca Raton.
11. PARZEN, E. (1954). On uniform convergence of families of sequences of random variables. University of California Publications in Statistics 2, 23-54.
12. REVUZ, D. (1975). MarkovChains. North-Holland, Amsterdam.
13. RUBINSTEIN, R. Y. (1981). Simulation and the Monte Carlo Method. Wiley, New York.