Rejection Control and Sequential Importance Sampling

Abstract We discuss ways of combining rejection sampling and importance sampling methods in Monte Carlo computations and demonstrate their usefulness in updating dynamic systems. Specifically, we propose the rejection controlled sequential importance sampling (RC-SIS) algorithm, which is designed to simultaneously reduce Monte Carlo variation and retain independent samples in sequential importance sampling. The proposed method is demonstrated by three examples taken from econometrics, hierarchical Bayes analysis, and digital telecommunications. They all show significant improvements over previous results.

[1]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[2]  Ray C. Fair,et al.  Methods of Estimation for Markets in Disequilibrium , 1972 .

[3]  T. Ferguson.  A Bayesian Analysis of Some Nonparametric Problems , 1973 .

[4]  N. Laird.  Nonparametric Maximum Likelihood Estimation of a Mixing Distribution , 1978 .

[5]  D. Berry,et al.  Empirical Bayes Estimation of a Binomial Parameter Via Mixtures of Dirichlet Processes , 1979 .

[6]  D. Donoho.  ON MINIMUM ENTROPY DECONVOLUTION , 1981 .

[7]  M. Rosenblatt,et al.  Deconvolution and Estimation of Transfer Function Phase and Coefficients for NonGaussian Linear Processes. , 1982 .

[8]  Richard E. Quandt,et al.  Econometric disequilibrium models , 1982 .

[9]  H. Scheraga,et al.  Use of buildup and energy‐minimization procedures to compute low‐energy structures of the backbone of enkephalin , 1985, Biopolymers.

[10]  T. Louis,et al.  Empirical Bayes Confidence Intervals Based on Bootstrap Samples , 1987 .

[11]  Richard E. Quandt,et al.  The Econometrics Of Disequilibrium , 1988 .

[12]  Jerry M. Mendel,et al.  Identification of nonminimum phase systems using higher order statistics , 1989, IEEE Trans. Acoust. Speech Signal Process..

[13]  J. Maritz,et al.  Empirical Bayes Methods, 2nd Edition. , 1990 .

[14]  David J. Spiegelhalter,et al.  Sequential updating of conditional probabilities on directed graphical structures , 1990, Networks.

[15]  J. Angus.  Empirical Bayes Methods , 1991 .

[16]  David F. Hendry,et al.  Likelihood Evaluation for Dynamic Latent Variables Models , 1992 .

[17]  G. Parisi,et al.  Simulated tempering: a new Monte Carlo scheme , 1992, hep-lat/9205018.

[18]  N. Gordon,et al.  Novel approach to nonlinear/non-Gaussian Bayesian state estimation , 1993 .

[19]  Persi Diaconis,et al.  Spectral Analysis for Discrete Longitudinal Data , 1994 .

[20]  A. Kong,et al.  Sequential imputation for multilocus linkage analysis. , 1994, Proceedings of the National Academy of Sciences of the United States of America.

[21]  Jun S. Liu,et al.  Sequential Imputations and Bayesian Missing Data Problems , 1994 .

[22]  M. Escobar.  Estimating Normal Means with a Dirichlet Process Prior , 1994 .

[23]  J. Besag,et al.  Bayesian Computation and Stochastic Systems , 1995 .

[24]  W. H. Wong,et al.  [Bayesian Computation and Stochastic Systems]: Comment , 1995 .

[25]  C. Geyer,et al.  Annealing Markov chain Monte Carlo with applications to ancestral inference , 1995 .

[26]  Rong Chen,et al.  Blind restoration of linearly degraded discrete signals by Gibbs sampling , 1995, IEEE Trans. Signal Process..

[27]  C. Robert.  Simulation of truncated normal variables , 2009, 0907.4010.

[28]  Jun S. Liu,et al.  Blind Deconvolution via Sequential Imputations , 1995 .

[29]  Walter R. Gilks,et al.  Comment on "Bayesian Computation and Stochastic Systems" , 1995 .

[30]  G. Casella,et al.  Rao-Blackwellisation of sampling schemes , 1996 .

[31]  Jun S. Liu.  Nonparametric hierarchical Bayes via sequential imputations , 1996 .

[32]  W H Wong,et al.  Dynamic weighting in Monte Carlo and optimization. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[33]  Jun S. Liu,et al.  Sequential Monte Carlo methods for dynamic systems , 1997 .

[34]  N. G. Best,et al.  Dynamic conditional independence models and Markov chain Monte Carlo methods , 1997 .