Bayesian methods: bayesian methods for simulation

This tutorial describes some ways that Bayesian methods address problems that arise during simulation studies. This includes quantifying uncertainty about input distributions and parameters, sensitivity analysis, and the selection of the best of several simulated alternatives. Focus is on illustrating the main ideas and their relevance to practical problems. Numerous citations for both introductory and more advanced material provide a launching pad into the Bayesian literature.

[1]  David Lindley,et al.  Bayesian Statistics, a Review , 1987 .

[2]  Lee W. Schruben,et al.  Uniform and bootstrap resampling of empirical distributions , 1993, WSC '93.

[3]  Bradley P. Carlin,et al.  BAYES AND EMPIRICAL BAYES METHODS FOR DATA ANALYSIS , 1996, Stat. Comput..

[4]  L. Wasserman,et al.  The Selection of Prior Distributions by Formal Rules , 1996 .

[5]  B. M. Hill,et al.  Theory of Probability , 1990 .

[6]  S. Gupta,et al.  Bayesian look ahead one-stage sampling allocations for selection of the best population , 1996 .

[7]  Peter W. Glynn,et al.  Problems in Bayesian analysis of stochastic simulation , 1986, WSC '86.

[8]  M. Degroot.  Optimal Statistical Decisions , 1970 .

[9]  Y. Rinott.  On two-stage selection procedures and related probability-inequalities , 1978 .

[10]  A. O'Hagan,et al.  Fractional Bayes factors for model comparison , 1995 .

[11]  H. Chipman,et al.  A Bayesian variable-selection approach for analyzing designed experiments with complex aliasing , 1997 .

[12]  Stephen E. Chick,et al.  New Procedures to Select the Best Simulated System Using Common Random Numbers , 2001, Manag. Sci..

[13]  Jin Wang,et al.  Approximation-assisted point estimation , 1997, Oper. Res. Lett..

[14]  Roger M. Cooke,et al.  Uncertainty in dispersion and deposition in accident consequence modeling assessed with performance-based expert judgment , 1994 .

[15]  James O. Berger,et al.  An overview of robust Bayesian analysis , 1994 .

[16]  Jon C. Helton.  Computational structure of a performance assessment involving stochastic and subjective uncertainty , 1996, Winter Simulation Conference.

[17]  Chun-Hung Chen,et al.  An empirical evaluation of several methods to select the best system , 1999, TOMC.

[18]  D. Madigan,et al.  Bayesian Model Averaging for Linear Regression Models , 1997 .

[19]  Chun-Hung Chen,et al.  An asymptotic allocation for simultaneous simulation experiments , 1999, WSC '99.

[20]  A. Raftery.  Bayesian Model Selection in Social Research , 1995 .

[21]  Chun-Hung Chen.  A lower bound for the correct subset-selection probability and its application to discrete-event system simulations , 1996, IEEE Trans. Autom. Control..

[22]  Stephen E. Chick,et al.  New Two-Stage and Sequential Procedures for Selecting the Best Simulated System , 2001, Oper. Res..

[23]  David Lindley,et al.  Optimal Statistical Decisions , 1971 .

[24]  Stephen E. Chick,et al.  Input Distribution Selection for Simulation Experiments: Accounting for Input Uncertainty , 2001, Oper. Res..

[25]  Walter R. Gilks,et al.  Adaptive rejection metropolis sampling , 1995 .

[26]  S. Chick.  Bayesian Analysis For Simulation Input And Output , 1997, Winter Simulation Conference Proceedings,.

[27]  J. Berger.  Statistical Decision Theory and Bayesian Analysis , 1988 .

[28]  Julie L. Swann,et al.  Simple Procedures for Selecting the Best Simulated System When the Number of Alternatives is Large , 2001, Oper. Res..

[29]  Dennis V. Lindley,et al.  An Introduction to Bayesian Inference and Decision , 1974 .

[30]  Bruce W. Schmeiser,et al.  Monte carlo estimation for guaranteed-coverage non-normal tolerance intervals , 1995 .

[31]  R.C.H. Cheng.  Regression metamodelling in simulation using Bayesian methods , 1999, WSC'99. 1999 Winter Simulation Conference Proceedings. 'Simulation - A Bridge to the Future' (Cat. No.99CH37038).

[32]  Barry L. Nelson,et al.  Statistical screening, selection, and multiple comparison procedures in computer simulation , 1998, 1998 Winter Simulation Conference. Proceedings (Cat. No.98CH36274).

[33]  Stephen E. Chick,et al.  Bayesian analysis for simulation input and output , 1997, WSC '97.

[34]  J. C. Helton,et al.  Computational structure of a performance assessment involving stochastic and subjective uncertainty , 1996, Proceedings Winter Simulation Conference.

[35]  Peter W. Glynn,et al.  Computing the distribution function of a conditional expectation via Monte Carlo: discrete conditioning spaces , 1999, WSC '99.

[36]  W. Gilks,et al.  Adaptive Rejection Metropolis Sampling Within Gibbs Sampling , 1995 .

[37]  Sylvia Richardson,et al.  Stochastic search variable selection , 1995 .

[38]  Sigrún Andradóttir,et al.  Applying Bayesian ideas in simulation , 2000, Simul. Pract. Theory.

[39]  E. Marian Scott.  Uncertainty and sensitivity studies of models of environmental systems , 1996, Winter Simulation Conference.

[40]  Peter Green,et al.  Markov chain Monte Carlo in Practice , 1996 .

[41]  A. Tversky,et al.  Judgment under Uncertainty: Heuristics and Biases , 1974, Science.

[42]  L. J. Savage,et al.  The Foundations of Statistics , 1955 .

[43]  Robert L. Winkler,et al.  An Introduction to Bayesian Inference and Decision , 1972 .

[44]  J. Berger,et al.  The Intrinsic Bayes Factor for Model Selection and Prediction , 1996 .

[45]  James R. Wilson,et al.  Graphical interactive simulation input modeling with bivariate Bézier distributions , 1995, TOMC.