Bayesian Analysis

Computational Enhancements to Bayesian Design of Experiments Using Gaussian Processes

Brian P. Weaver, Brian J. Williams, Christine M. Anderson-Cook, and David M. Higdon

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Bayesian design of experiments is a methodology for incorporating prior information into the design phase of an experiment. Unfortunately, the typical Bayesian approach to designing experiments is both numerically and analytically intractable without additional assumptions or approximations. In this paper, we discuss how Gaussian processes can be used to help alleviate the numerical issues associated with Bayesian design of experiments. We provide an example based on accelerated life tests and compare our results with large-sample methods.

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Bayesian Anal., Volume 11, Number 1 (2016), 191-213.

First available in Project Euclid: 4 March 2015

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Bayesian design of experiments Gaussian processes accelerated life tests preposterior expectation expected quantile improvement


Weaver, Brian P.; Williams, Brian J.; Anderson-Cook, Christine M.; Higdon, David M. Computational Enhancements to Bayesian Design of Experiments Using Gaussian Processes. Bayesian Anal. 11 (2016), no. 1, 191--213. doi:10.1214/15-BA945.

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  • Adler, R. J. (1981). The Geometry of Random Fields. New York: J. Wiley.
  • Anderson-Cook, C. M., Graves, T. L., and Hamada, M. S. (2008). “Resource allocation: Sequential design for analyses involving several types of data.” In: IEEE International Conference on Industrial Engineering and Engineering Management, 2008. IEEM 2008, 571–575. IEEE.
  • — (2009). “Resource allocation for reliability of a complex system with aging components.” Quality and Reliability Engineering International, 25(4): 481–494.
  • Chaloner, K. and Larntz, K. (1992). “Bayesian design for accelerated life testing.” Journal of Statistical Planning and Inference, 33(2): 245–259.
  • Chaloner, K. and Verdinelli, I. (1995). “Bayesian Experimental Design: A Review.” Statistical Science, 10(3): pp. 273–304. URL:
  • Chib, S. and Greenberg, E. (1995). “Understanding the Metropolis–Hastings algorithm.” The American Statistician, 327–335.
  • Clyde, M., Müller, P., and Parmigiani, G. (1995). “Optimal Design for Heart Defibrillators.” In: Gatsonis, C., Hodges, J., Kass, R., and Singpurwalla, N. (eds.), Case Studies in Bayesian Statistics 2, 278–292. Springer.
  • Cramér, H. and Leadbetter, M. R. (1967). Stationary and Related Stochastic Processes. New York: J. Wiley.
  • Drovandi, C. C., McGree, J. M., and Pettitt, A. N. (2013). “Sequential Monte Carlo for Bayesian sequentially designed experiments for discrete data.” Computational Statistics and Data Analysis, 57(1): 320–335.
  • — (2014). “A sequential Monte Carlo algorithm to incorporate model uncertainty in Bayesian sequential design.” Journal of Computational and Graphical Statistics, 23(1): 3–24.
  • Escobar, L. and Meeker, W. (1994). “Algorithm AS 292: Fisher information matrix for the extreme value, normal and logistic distributions and censored data.” Journal of the Royal Statistical Society. Series C (Applied Statistics), 43(3): 533–540.
  • Etzioni, R. and Kadane, J. B. (1993). “Optimal experimental design for another’s analysis.” Journal of the American Statistical Association, 88(424): 1404–1411.
  • Gramacy, R. and Lee, H. (2010). “Optimization under Unknown Constraints.” In: Bernardo, J. M., Bayarri, M. J., Berger, J. O., P, D. A., Heckerman, A. F. M., and Smith, M. W. (eds.), Bayesian Statistics. Oxford: Oxford University Press, 9th edition.
  • Hamada, M., Martz, H., Reese, C., and Wilson, A. (2001). “Finding near-optimal Bayesian experimental designs via genetic algorithms.” The American Statistician, 55(3): 175–181.
  • Huan, X. and Marzoukm Y. M. (2013). “Simulation-based optimal Bayesian experimental design for nonlinear systems.” Journal of Computational Physics, 232(1): 288–317.
  • Huang, D., Allen, T. T., Notz, W. I., and Zeng, N. (2006). “Global optimization of stochastic black-box systems via sequential Kriging meta-models.” Journal of Global Optimization, 34(3): 441–466.
  • Jones, D. R., Schonlau, M., and Welch, W. J. (1998). “Efficient Global Optimization of Expensive Black-Box Functions.” Journal of Global Optimization, 13: 455–492.
  • Lindley, D. V. (1972). Bayesian Statistics – A Review. SIAM.
  • Matérn, B. (1986). Spatial Variation. Springer Verlag, second edition.
  • McKay, M. D., Beckman, R. J., and Conover, W. J. (1979). “Comparison of three methods for selecting values of input variables in the analysis of output from a computer code.” Technometrics, 21(2): 239–245.
  • Meeker, W. and Escobar, L. (1998). Statistical methods for reliability data. John Wiley and Sons, INC.
  • Müller, P. (1999). “Simulation Based Optimal Design.” In: Bernardo, J. M., Berger, J. O., Dawid, A. P., and Smith, A. F. M. (eds.), Bayesian Statistics 6, 459–474. Oxford University Press.
  • Picard, R. and Williams, B. (2013). “Rare event estimation for computer models.” The American Statistician, 67(1): 22–32.
  • Picheny, V., Ginsbourger, D., Richet, Y., and Caplin, G. (2013). “Quantile-Based Optimization of Noisy Computer Experiments With Tunable Precision.” Technometrics, 55: 2–13.
  • Raiffa, H. and Schlaifer, R. (1961). Applied Statistical Decision Theory. Division of Research, Graduate School of Business Administration.
  • Robert, C. and Casella, G. (2004). Monte Carlo statistical methods. Springer Verlag.
  • Roustant, O., Ginsbourger, D., and Deville, Y. (2012). “DiceKriging, DiceOptim: Two R Packages for the Analysis of Computer Experiments by Kriging-Based Metamodeling and Optimization.” Journal of Statistical Software, 51: 1–55.
  • Santner, T. J., Williams, B. J., and Notz, W. I. (2003). The Design and Analysis of Computer Experiments. New York: Springer.
  • Tsutakawa, R. K. (1972). “Design of experiment for bioassay.” Journal of the American Statistical Association, 67(339): 584–590.
  • Zhang, Y. and Meeker, W. (2006). “Bayesian methods for planning accelerated life tests.” Technometrics, 48(1): 49–60.