## Bayesian Analysis For Simulation Input And Output (1997)

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Citations: | 20 - 8 self |

### BibTeX

@MISC{Chick97bayesiananalysis,

author = {Stephen Chick},

title = {Bayesian Analysis For Simulation Input And Output},

year = {1997}

}

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### Abstract

The paper summarizes some important results at the intersection of the fields of Bayesian statistics and stochastic simulation. Two statistical analysis issues for stochastic simulation are discussed in further detail from a Bayesian perspective. First, a review of recent work in input distribution selection is presented. Then, a new Bayesian formulation for the problem of output analysis for a single system is presented. A key feature is analyzing simulation output as a random variable whose parameters are an unknown function of the simulation's inputs. The distribution of those parameters is inferred from simulation output via Bayesian response-surface methods. A brief summary of Bayesian inference and decision making is included for reference.

### Citations

1245 |
Simulation Modeling and Analysis
- Law, Kelton
- 2000
(Show Context)
Citation Context ...input distributions, in that much focus has been on estimating means of output, rather than the assessing the entire distribution using parameter estimation and goodness-of-fit techniques. (Although (=-=Law and Kelton, 1991-=-; Glynn, 1996) among others discuss quantiles of simulation output.) The entire output distribution can be important to a decision maker (Law and Kelton, 1991; Banks et al., 1996). From the distributi... |

1240 |
Statistical decision theory and Bayesian analysis. Springer series in Statistics
- Berger
- 1985
(Show Context)
Citation Context ...a given hypothesis is true (e.g. p Hjx (H 0 )). Bayesian statistics is often used in conjunction with decision making where the objective is to maximize the expected utility of a decision (see e.g., (=-=Berger, 1985-=-) or (de Groot, 1970)). This paper refers to the mean of output values rather than expected utility, as current work in stochastic simulation analysis generally focuses on estimation of means. 3 LITER... |

983 | Bayes factors
- Kass, Raftery
- 1995
(Show Context)
Citation Context ... arise in Bayesian analysis. 4 INPUT DISTRIBUTION SELECTION Bayesian formulations for statistical distribution selection have been applied to a number of fields (Draper, 1995; Madigan and York, 1995; =-=Kass and Raftery, 1995-=-; Raftery, 1995; Volinsky et al., 1996). A central idea is that all uncertainty, including distribution uncertainty, is to be represented by probability statements. The formulation presented by Chick ... |

693 | Optimal Statistical Decisions - DeGroot - 1970 |

546 |
Markov Chain Monte Carlo in practice
- Gilks, Richardson, et al.
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(Show Context)
Citation Context ... chain methods. Simulation techniques are therefore playing an important role in making a Bayesian analysis computationally tractable (Chen and Schmeiser, 1993). Gilks, Richardson, and Spiegelhalter (=-=Gilks et al., 1996-=-) provide a comprehensive review of many of the theoretical, philosophical and practical issues related to Markov chain Monte Carlo (MCMC) techniques. The MCMC WWW site (http://www.stats.bris.ac.uk/MC... |

351 |
Influence diagrams
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- 1981
(Show Context)
Citation Context ... formulation of the relationships between simulation inputs and outputs is summarized in Fig. 2. The figure is drawn as a Bayesian network, where probabilistic dependencies are represented with arcs (=-=Howard and Matheson, 1984-=-). The figure represents that for replication r, simulated variates X r i depend on the input parametersand uniform variates U r j from the simulator; the outputsO r can be described in terms of param... |

256 | Bayesian Model Selection in Social Research
- Raftery
- 1995
(Show Context)
Citation Context ... Bayesian analysis. 4 INPUT DISTRIBUTION SELECTION Bayesian formulations for statistical distribution selection have been applied to a number of fields (Draper, 1995; Madigan and York, 1995; Kass and =-=Raftery, 1995-=-; Raftery, 1995; Volinsky et al., 1996). A central idea is that all uncertainty, including distribution uncertainty, is to be represented by probability statements. The formulation presented by Chick ... |

226 | Bayesian graphical models for discrete data
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- 1995
(Show Context)
Citation Context ...erior distributions that arise in Bayesian analysis. 4 INPUT DISTRIBUTION SELECTION Bayesian formulations for statistical distribution selection have been applied to a number of fields (Draper, 1995; =-=Madigan and York, 1995-=-; Kass and Raftery, 1995; Raftery, 1995; Volinsky et al., 1996). A central idea is that all uncertainty, including distribution uncertainty, is to be represented by probability statements. The formula... |

172 | Bayesian experimental design: a review
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- 1995
(Show Context)
Citation Context ...rthogonal arrays of computer experiments, and select the array which gives the maximum expected information gain. They iterate with more refined computer models as necessary. Chaloner and Verdinelli (=-=Chaloner and Verdinelli, 1995-=-) provide a thorough overview of Bayesian experimental design in general. 3.2 Simulation for Bayesian analysis Bayesian statistics presents a number of challenges for numerical analysis, notably for p... |

162 |
The selection of prior distributions by formal rules
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- 1996
(Show Context)
Citation Context ...m used for providing confidence intervals for the MLE of frequentist approaches (Leemis, 1995). A review of work investigating the problem of automatically selecting an appropriate prior is given by (=-=Kass and Wasserman, 1996-=-). A discussion of the robustness of this selection process with respect to poor choices of prior distributions is given by Berger (Berger, 1994). The problem of not including the correct distribution... |

144 | Discrete-Event System Simulation - Banks, Carson, et al. - 2001 |

91 |
Bayesian Prediction of Deterministic Functions, with Application to the Design and Analysis of Computer Experiments
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(Show Context)
Citation Context ... Evaluations of \Xi at the points x 0 ; : : : ; xn and Bayes rule are used to infer the values of the OE j (and therefore \Xi) at other values of the input x. Currin, Mitchell, Morris, and Ylvisakir (=-=Currin et al., 1991-=-) provide results for selecting points x i which provide maximal inferential power for a special case of the Kriging model. Morris, Mitchell, and Ylvisakir (Morris et al., 1993) extend the framework t... |

67 | Computer experiments
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(Show Context)
Citation Context ...re used to infer the parameters of a postulated functional form for the algorithm's output. The design of computer experiments to learn the shape of the function is a central focus. Koehler and Owen (=-=Koehler and Owen, 1995-=-) provide a review of techniques in this well-explored area. One formulation is the Kriging model, which assumes that the unknown real-valued function is \Xi(x) = N X j=1 OE j h j (x) + Z(x); where th... |

48 |
Bayesian design and analysis of computer experiments: Use of derivatives in surface prediction”. Technometrics 35:243–255
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(Show Context)
Citation Context ... Morris, and Ylvisakir (Currin et al., 1991) provide results for selecting points x i which provide maximal inferential power for a special case of the Kriging model. Morris, Mitchell, and Ylvisakir (=-=Morris et al., 1993-=-) extend the framework to accomodate simulation output which returns derivatives of \Xi as well as \Xi for each function evaluation. Osio and Amon (Osio and Amon, 1997) expand the problem to plan comp... |

37 |
An overview of robust Bayesian analysis
- Berger
- 1994
(Show Context)
Citation Context ...selecting an appropriate prior is given by (Kass and Wasserman, 1996). A discussion of the robustness of this selection process with respect to poor choices of prior distributions is given by Berger (=-=Berger, 1994-=-). The problem of not including the correct distribution in the original set of distributions is discussed in Sec. 7. The probabilistic interpretation of distribution correctness is not without its de... |

34 |
Likelihood
- Edwards
- 1992
(Show Context)
Citation Context ...ding the correct distribution in the original set of distributions is discussed in Sec. 7. The probabilistic interpretation of distribution correctness is not without its detractors. See for example (=-=Edwards, 1984-=-). 5 OUTPUT ANALYSIS Consider the problem of analyzing the output from a single simulated system (see (Chick, 1997) for an extension to multiple systems). Focus here is on output which is independent ... |

33 | Methods for approximating integrals in statistics with special emphasis on Bayesian integration
- Evans, Swartz
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(Show Context)
Citation Context ...tion for Bayesian analysis Bayesian statistics presents a number of challenges for numerical analysis, notably for predictive inference when the denominator in Eq. 1 is needed. A recent survey paper (=-=Evans and Swartz, 1995-=-) indicates that significant progress has been made using five general techniques: asymptotic methods, importance sampling, adaptive importance sampling, multiple quadrature, and Markov chain methods.... |

29 | Bayesian Model Averaging in Proportional Hazard Models: Assessing the Risk of a Stroke
- Volinsky, Madigan, et al.
- 1997
(Show Context)
Citation Context ...STRIBUTION SELECTION Bayesian formulations for statistical distribution selection have been applied to a number of fields (Draper, 1995; Madigan and York, 1995; Kass and Raftery, 1995; Raftery, 1995; =-=Volinsky et al., 1996-=-). A central idea is that all uncertainty, including distribution uncertainty, is to be represented by probability statements. The formulation presented by Chick (Chick, 1996) can be summarized as fol... |

19 |
Performance of the Gibbs, Hit-and-Run and Metropolis Samplers
- Chen, Schmeiser
- 1993
(Show Context)
Citation Context ...ng, adaptive importance sampling, multiple quadrature, and Markov chain methods. Simulation techniques are therefore playing an important role in making a Bayesian analysis computationally tractable (=-=Chen and Schmeiser, 1993-=-). Gilks, Richardson, and Spiegelhalter (Gilks et al., 1996) provide a comprehensive review of many of the theoretical, philosophical and practical issues related to Markov chain Monte Carlo (MCMC) te... |

17 |
An Engineering Design Methodology with Multistage Bayesian Surrogates and Optimal Sampling
- Osio, Amon
- 1996
(Show Context)
Citation Context ...Morris, Mitchell, and Ylvisakir (Morris et al., 1993) extend the framework to accomodate simulation output which returns derivatives of \Xi as well as \Xi for each function evaluation. Osio and Amon (=-=Osio and Amon, 1997-=-) expand the problem to plan computer experiments where several functions of differing levels of accuracy could be programmed, the more simplistic models being quicker but less accurate. They evaluate... |

17 |
Hepatitis B: a case study in MCMC methods
- Spiegelhalter, Best, et al.
- 1996
(Show Context)
Citation Context ...ical, philosophical and practical issues related to Markov chain Monte Carlo (MCMC) techniques. The MCMC WWW site (http://www.stats.bris.ac.uk/MCMC/) contains a significant collection of references. (=-=Spiegelhalter et al., 1996-=-) provide a package called BUGS to perform Bayesian inference via MCMC methods (mailto:bugs@mrc-bsu.cam.ac.uk). The software can be used to generate samples from posterior distributions that arise in ... |

16 | Importance sampling for Monte Carlo estimation of quantiles
- Glynn
- 1996
(Show Context)
Citation Context ...n that much focus has been on estimating means of output, rather than the assessing the entire distribution using parameter estimation and goodness-of-fit techniques. (Although (Law and Kelton, 1991; =-=Glynn, 1996-=-) among others discuss quantiles of simulation output.) The entire output distribution can be important to a decision maker (Law and Kelton, 1991; Banks et al., 1996). From the distribution, any quant... |

12 |
Assessment and propogation of model uncertainty (with discussion
- Draper
- 1995
(Show Context)
Citation Context ...ples from posterior distributions that arise in Bayesian analysis. 4 INPUT DISTRIBUTION SELECTION Bayesian formulations for statistical distribution selection have been applied to a number of fields (=-=Draper, 1995-=-; Madigan and York, 1995; Kass and Raftery, 1995; Raftery, 1995; Volinsky et al., 1996). A central idea is that all uncertainty, including distribution uncertainty, is to be represented by probability... |

10 | Selecting the best system: A decision-theoretic approach
- Chick
- 1997
(Show Context)
Citation Context ...etation of distribution correctness is not without its detractors. See for example (Edwards, 1984). 5 OUTPUT ANALYSIS Consider the problem of analyzing the output from a single simulated system (see (=-=Chick, 1997-=-) for an extension to multiple systems). Focus here is on output which is independent from simulation replication to replication (batch mean output is not considered). Curiously, simulation output dat... |

8 |
Problems in Bayesian Analysis of Stochastic Simulation
- Glynn
- 1986
(Show Context)
Citation Context ...te-event dynamic simulation, simulation input modeling, distribution selection, simulation output modeling, Bayesian statistics, Bayesian response surface methods. 1 INTRODUCTION A decade ago, Glynn (=-=Glynn, 1986-=-) argued that `Bayesian statistical methodology has an important role to play in the theory and practice of stochastic simulation'. At present, however, the number of contributions of applying Bayesia... |

5 |
Applying Bayesian ideas in simulation
- Andradóttir, Bier
- 1996
(Show Context)
Citation Context ...on. He also developed extensions to Latin hypercube sampling to provide variance reduction even when the input distribution (and therefore the number of parameters) is unknown. Andrad'ottir and Bier (=-=Andrad'ottir and Bier, 1996-=-) discuss possible roles of Bayesian analysis in model validation, and output analysis with both normal and truncated normal distributions. They present results on importance sampling when the paramet... |

3 |
A Bayesian batch means methodology for analysis of simulation output
- Andrews, Schriber
- 1983
(Show Context)
Citation Context ... stochastic systems and the simulation of deterministic, but unknown systems. For the analysis of stochastic simulations the literature is not extensive. Stochastic simulations. Andrews and Schriber (=-=Andrews and Schriber, 1983-=-) appear to be the first to discuss modeling simulation output with a Bayesian formalism. They construct a point estimator and a Bayesian confidence interval for the mean of batchrun simulation output... |

3 |
Input Modeling for Discrete-Event Simulation
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- 1995
(Show Context)
Citation Context ...provides an example where the approximation worked well. The ~ \Sigma m term is analagous to the information matrix term used for providing confidence intervals for the MLE of frequentist approaches (=-=Leemis, 1995-=-). A review of work investigating the problem of automatically selecting an appropriate prior is given by (Kass and Wasserman, 1996). A discussion of the robustness of this selection process with resp... |

1 |
Validation of microeconomic simulation: A comparison of sampling theory and Bayesian methods
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- 1986
(Show Context)
Citation Context ...imulation output. Specific assumptions include a Gaussian prior for the mean, and a stationary Gaussian process with autocorrelated output from batch to batch. Andrews, Birdsall, Gentner, and Spivey (=-=Andrews et al., 1986-=-) investigate Bayesian techniques for validation of simulation output. Glynn (Glynn, 1986) describes an attractive, general framework for modeling a generalized semiMarkov process (GSMP) when the para... |

1 |
Input distribution selection and variance reduction for discrete-event dynamic simulation: A Bayesian perspective. submitted to Operations Research
- Chick
- 1996
(Show Context)
Citation Context ...zation problem to select a prior distribution satisfying certain desirable properties. In this respect, they perform a Bayesian robustness analysis for analyzing Monte Carlo simulation output. Chick (=-=Chick, 1996-=-) addresses the problem of selecting an appropriate input distribution (e.g. exponential, gamma) using Bayesian hypothesis testing, as well as the problem of parameter uncertainty for a given input di... |

1 | A MultiModel, Bayesian, Resampling, Sequential Experimental Design for Response Surface Estimation - Dornbusch, L - 1994 |

1 |
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Citation Context ... He notes that the probability distribution of the output depends on the prior distribution of the input parameters, and comments on potential research directions. Nelson, Schmeiser, Taaffe and Wang (=-=Nelson et al., 1997-=-) evaluated several techniques for combining a deterministic approximation with a stochastic simulation estimator, among them a Bayesian analysis (Gaussian distribution) for a point estimator. Wang an... |

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1 | Amulti-model, Bayesian, resampling, sequential experimental design for responsesurfaceestimation. Ph.D.thesis,University ofMichigan,AnnArbor.DeptartmentofIndustrial andOperations Engineering,unpublished. Leemis,L.M.1995.Inputmodelingfordiscrete-event simu - Ledersnaider - 1994 |

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