Optimal bayesian design by inhomogeneous Markov chain simulation

Journal of the American Statistical Association

Volumn 99, Issue 467, 2004, Pages 788-798

  Müller, Peter ^a   Sansó, Bruno ^b,c   De Iorio, Maria ^d  

^a UNIVERSITY OF TEXAS   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c UNIVERSIDAD SIMÓN BOLÍVAR   (Venezuela)

^d IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Decision theory; Expected utility maximization; Markov chain Monte Carlo; Optimal design

Indexed keywords

EID: 4944254628     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/016214504000001123     Document Type: Article

References (39)

1. Berger, J. O., and Barbieri, M. M. (2004), "Optimal Predictive Model Selection," The Annals of Statistics, 32, 870-897.
2. Berry, D. (1993), "A Case for Bayesianism in Clinical Trials" (with discussion), Statistics in Medicine, 12, 1377-1404.
3. Berry, D. A., and Stangl, D. K. (eds.) (1996), Bayesian Biostatistics, New York: Marcel Dekker.
4. Bielza, C., Müller, P., and Insua, D. R. (1999), "Monte Carlo Methods for Decision Analysis With Applications to Influence Diagrams," Management Science, 45, 995-1007.
5. Bras, R. L., and Rodríguez-Iturbe, I. (1985), Random Functions and Hydrology, Reading, MA: Addison-Wesley.
6. Brockwell, A. E., and Kadane, J. B. (2003), "Sequential Analysis by Gridding Sufficient Statistics," Journal of Computational and Graphical Statistics, 12, 566-584.
7. Brown, P. J., Fearn, T., and Vannucci, M. (1999), "The Choice of Variables in Multivariate Regression: A Non-Conjugate Bayesian Decision Theory Approach," Biometrika, 86, 635-648.
8. Carlin, B., Kadane, J., and Gelfand, A. (1998), "Approaches for Optimal Sequential Decision Analysis in Clinical Trials," Biometrics, 54, 964-975.
9. Caselton, W. F., Kan, L., and Zidek, J. (1992), "Quality Data Networks That Minimize Entropy," in Statistics in the Environment and Earth Sciences, eds. P. Guttorp and A. Walden, London: Griffin, pp. 10-38.
10. Chaloner, K., and Verdinelli, I. (1995), "Bayesian Experimental Design: A Review," Statistical Science, 10, 273-304.
11. Chipman, H. A., George, E. I., and McCulloch, R. E. (2001), Model Selection, Heyward, CA: IMS.
12. Clayton, M. K., Shepherd, J., Hsiao, C. F., and Li, S. H. (1999), "Bayesian Sequential Design of a Network of Sensors," technical report, University of Wisconsin, Dept. of Statistics.
13. Clyde, M., and George, E. I. (2003), "Model Uncertainty," technical report, Duke University, ISDS.
14. DeGroot, M. (1970), Optimal Statistical Decisions, New York: McGraw-Hill, Chap. 7.
15. Doucet, A., Godsill, S., and Robert, C. (2002), "Marginal Maximum a Posteriori Estimation Using Markov Chain Monte Carlo," Statistics and Computing, 77-84.
16. Etzioni, R., and Kadane, J. (1993), "Optimal Experimental Design for Another's Analysis," Journal of the American Statistical Association, 88, 1401-1411.
17. Fei, L., and Berliner, L. M. (1991), "Asymptotic Properties of Stochastic Probing for Global Optimization: The Finite Case," technical report, Ohio State University, Dept. of Statistics.
18. Fouskakis, D., and Draper, D. (2002), "Stochastic Optimization: A Review," International Statistical Review, 70, 315-350.
19. Geman, S., and Geman, A. (1984), "Stochastic Relaxation, Gibbs Distributions and the Bayesian Restoration of Images," IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721-741.
20. George, E. I., and McCulloch, R. E. (1993), "Variable Selection via Gibbs Sampling," Journal of the American Statistical Association, 88, 881-889.
21. Guttorp, P., Le, N., and Zidek, J. (1994), "Using Entropy in the Redesign of an Environmental Monitor Network," in Multivariate Environmental Statistics, eds. G. Patil and C. Rao, London: Elsevier Science, pp. 175-202.
22. Handcock, M., and Stein, M. (1993), "A Bayesian Analysis of Kriging," Technometrics, 35, 403-410.
23. Higdon, D. M. (2002), "Space and Space-Time Modeling Using Process Convolutions," in Quantitative Methods for Current Environmental Issues, eds. C. W. Anderson, V. Barnett, P. C. Chatwin, and A. H. El-Shaarawi, New York: Springer-Verlag, pp. 37-54.
24. Isaacson, D. L., and Madsen, R. W. (1976), Markov Chains: Theory and Applications, New York: Wiley.
25. Johnson, M. E., Moore, L. M., and Ylvisaker, D. (1990), "Minimax and Maximin Distance Designs," Journal of Statistical Planning and Inference, 26, 131-148.
26. Laud, P. W., Berliner, L. M., and Goel, P. K. (1992), "A Stochastic Probing Algorithm for Global Optimization," Journal of Global Optimization, 2, 209-224.
27. Müller, A. (1999), "Simulation-Based Optimal Design," in Bayesian Statistics 6, eds. J. M. Bernardo, J. O. Berger, P. Dawid, and A. F. M. Smith, Oxford, U.K.: Oxford University Press, pp. 459-474.
28. Müller, P., and Parmigiani, G. (1996), "Optimal Design via Curve Fitting of Monte Carlo Experiments," Journal of the American Statistical Association, 90, 1322-1330.
29. Nychka, D., and Saltzman, N. (1998), "Design of Air-Quality Monitoring Networks," in Case Studies in Environmental Statistics, eds. D. Nychka, W. Piegorsch, and L. Cox, New York: Springer-Verlag, pp. 51-76.
30. Raiffa, H., and Schlaifer, R. (1961), Applied Statistical Decision Theory, Boston: Harvard University Press.
31. Robert, C. P., Doucet, A., and Godsill, S. J. (1999), "Marginal MAP Estimation Using Markov Chain Monte Carlo," technical report, CREST, INSEE.
32. Sansó, B., and Guenni, L. (1999), "Venezuelan Rainfall Data Analyzed Using a Bayesian Space-Time Model," Applied Statistics, 48, 345-362.
33. Sansó, B., and Müller, P. (1999), "Redesigning a Network of Rainfall Stations," in Case Studies in Bayesian Statistics, Vol. 4, eds. C. Gatsonis, R. Kass, B. Carlin, A. Carriquiry, A. Gelman, I. Verdinelli, and M. West, New York: Springer-Verlag, pp. 497-510.
34. Sha, N., Vannucci, M., Brown, P. J., Trower, M. K., Amphlett, G., and Falciani, F. (2003), "Gene Selection in Arthritis Classification With Large-Scale Microarray Expression Profiles," Comparative and Functional Genomics, 4, 171-181.
35. Spiegelhalter, D. J., Freedman, L. S., and Parmar, M. K. B. (1994), "Bayesian Approaches to Randomized Trials," Journal of the Royal Statistical Society, Ser. A, 157, 357-387.
36. Sun, D., Tsutakawa, R. K., and Lu, W.-S. (1996), "Bayesian Design of Experiment for Quantal Responses: What Is Promised versus What Is Delivered," Journal of Statistical Planning and Inference, 52, 289-306.
37. Tierney, L. (1994), "Markov Chains for Exploring Posterior Distributions," The Annals of Statistics, 22, 1701-1728.
38. van Laarhoven, P., and Aarts, E. (1987), Simulated Annealing: Theory and Applications, Dordrecht: D. Reidel.
39. Zidek, J. V., Sun, W., and Le, N. D. (2000), "Designing and Integrating Composite Networks for Monitoring Multivariate Gaussian Pollution Fields," Applied Statistics, 49, 63-79.