On a likelihood approach for Monte Carlo integration

Journal of the American Statistical Association

Volumn 99, Issue 468, 2004, Pages 1027-1036

  Tan, Zhiqiang ^a  

^a JOHNS HOPKINS BLOOMBERG SCHOOL OF PUBLIC HEALTH   (United States)

Author keywords

Bridge sampling; Control variate; Importance sampling; Stratified sampling

Indexed keywords

EID: 10844294119     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/016214504000001664     Document Type: Article

References (16)

1. Cochran, W. G. (1977), Sampling Techniques (3rd ed.), New York: Wiley.
2. Geyer, C. J. (1994), Estimating Normalizing Constants and Reweighing Mixtures in Markov Chain Monte Carlo, technical report, University of Minnesota, School of Statistics.
3. Gill, R., Vardi, Y., and Wellner, J. (1988), Large Sample Theory of Empirical Distributions in Biased Sampling Models, The Annals of Statistics, 16, 1069-1112.
4. Glynn, P. W., and Szechtman, R. (2000), Some New Perspectives on the Method of Control Variates, in Monte Carlo and Quasi-Monte Carlo Methods, eds. K.-T. Fang, F. J. Hickernell, and H. Niederreiter, New York: Springer-Verlag, pp. 27-49.
5. Hammersley, J. M., and Handscomb, D. C. (1964), Monte Carlo Methods, London: Methuen.
6. Hesterberg, T. (1995), Weighted Average Importance Sampling and Defensive Mixture Distributions, Technometrics, 37, 185-194.
7. Kong, A., McCullagh, P., Meng, X.-L., Nicolae, D., and Tan, Z. (2003), A Theory of Statistical Models for Monte Carlo Integration (with discussion), Journal of the Royal Statistical Society, Ser. B, 65, 585-618.
8. Meng, X.-L., and Wong, W. H. (1996), Simulating Ratios of Normalizing Constants via a Simple Identity: A Theoretical Explanation, Statistica Sinica, 6, 831-860.
9. Niemiro, W. (1992), Asymptotics for M-Estimators Defined by Convex Minimization, The Annals of Statistics, 20, 1514-1533.
10. Owen, A. (2001), Empirical Likelihood, New York: Chapman & Hall.
11. Owen, A., and Zhou, Y. (2000), Safe and Effective Importance Sampling, Journal of the American Statistical Association, 95, 135-143.
12. Tan, Z. (2003a), Monte Carlo Integration With Markov Chain, working paper, Johns Hopkins University, Department of Biostatistics.
13. _ (2003b), Monte Carlo Integration With Acceptance-Rejection, working paper, Johns Hopkins University, Department of Biostatistics.
14. van der Vaart, A. W. (1998), Asymptotic Statistics, Cambridge, U.K.: Cambridge University Press.
15. Vardi, Y (1985), Empirical Distributions in Selection Bias Models, The Annals of Statistics, 25, 178-203.
16. Veach, E. and Guibas, L. (1995), Optimally Combining Sampling Techniques for Monte Carlo Rendering, in SIGGRAPH'95 Conference Proceedings, Reading, MA: Addison-Wesley, pp. 419-428.