Steps to implement Bayesian input distribution selection

There are known pragmatic and theoretical difficulties associated with some standard approaches for input distribution selection for discrete-event simulations. One difficulty is a systematic underestimate of the variance of the expected simulation output that comes from not knowing the 'true' parameter values. Another is a lack of quantification of the probability that a given distribution is best. Bayesian methods have been proposed as an alternative, but acceptance has not yet been achieved, in part because of increased computational demands, as well as challenges posed by the specification of prior distributions. In this paper, we show that responses to questions like those already asked and answered in practice can be used to develop prior distributions for a wide class of models. Further, we illustrate techniques for addressing some computational difficulties thought to be associated with the implementation of Bayesian methodology.

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

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

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

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

[5]  Lawrence Leemis Input modeling for discrete-event simulation , 1995, WSC '95.

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

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

[8]  J. Berger,et al.  Testing Precise Hypotheses , 1987 .

[9]  Russell C. H. Cheng,et al.  Selecting input models , 1994, Proceedings of Winter Simulation Conference.

[10]  J. York,et al.  Bayesian Graphical Models for Discrete Data , 1995 .

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

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

[13]  S. Chick Selecting The Best System: A Decision-theoretic Approach , 1997, Winter Simulation Conference Proceedings,.

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

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

[16]  M. Evans,et al.  Methods for Approximating Integrals in Statistics with Special Emphasis on Bayesian Integration Problems , 1995 .

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

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