Robust Bayesian Analysis

Handbook of Statistics

Volumn 25, Issue , 2005, Pages 623-667

  Ruggeri, Fabrizio ^a   Ríos Insua, David ^a   Martín, Jacinto ^a  

^a NONE

Author keywords

algorithms; applications; Bayesian robustness; prior likelihood loss robustness; sensitivity analysis

Indexed keywords

EID: 59749104376     PISSN: 01697161     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0169-7161(05)25021-6     Document Type: Review

References (126)

1. Albert J., Delampady M., and Polasek W. A class of distributions for robustness studies. J. Statist. Plann. Inference 28 (1991) 291-304
2. Arias, J.P. (2002). The non-dominated set in robust Bayesian decision theory (in Spanish). Ph.D. Dissertation, Department of Mathematics, Universidad de Extremadura, Spain, 2002
3. Arias J.P., and Martín J. Uncertainty in beliefs and preferences: Conditions for optimal alternatives. Ann. Math. Artificial Intelligence 35 (2002) 3-10
4. Arias, J.P., Martín, J., Suárez, A. (2004a). Bayesian robustness with convex loss functions. Technical Report, Dept. of Mathematics, Universidad de Extremadura, Spain
5. Arias, J.P., Martín, J., Ruggeri, F., Suárez, A. (2004b). Optimal actions in problems with convex loss functions. Technical Report 2-MI, CNR-IMATI Milano, Italy
6. Basu, S. (1992). Variations of posterior expectations for symmetric unimodal priors in a distribution band. Technical Report 214, Department of Statistics and Applied Probability, University of California, Santa Barbara, USA
7. Basu S. Ranges of posterior probability over a distribution band. J. Statist. Plann. Inference 44 (1995) 149-166
8. Basu S. Local sensitivity, functional derivatives and nonlinear posterior quantities. Statist. Decisions 14 (1996) 405-418
9. Basu, S., DasGupta, A. (1990). Bayesian analysis under distribution bands. Technical Report 90-48, Department of Statistics, Purdue University, USA
10. Basu S., and DasGupta A. Robust Bayesian analysis with distribution bands. Statist. Decisions 13 (1995) 333-349
11. Basu S., Jammalamadaka S.R., and Liu W. Local posterior robustness with parametric priors: Maximum and average sensitivity. In: Heidlbreder G. (Ed). Maximum Entropy and Bayesian Methods (1996), Kluwer Academic, Dordrecht, The Netherlands
12. Bell D. Risk, return and utility. Management Sci. 41 (1995) 23-30
13. Berger J.O. The robust Bayesian viewpoint (with discussion). In: Kadane J. (Ed). Robustness of Bayesian Analysis (1984), North-Holland, Amsterdam, The Netherlands
14. Berger J.O. Statistical Decision Theory and Bayesian Analysis. second ed (1985), Springer-Verlag, New York, USA
15. Berger J.O. Robust Bayesian analysis: Sensitivity to the prior. J. Statist. Plann. Inference 25 (1990) 303-328
16. Berger J.O. An overview of robust Bayesian analysis. Test 3 (1994) 5-58
17. Berger J.O., and Berliner L.M. Robust Bayes and empirical Bayes analysis with ε-contaminated priors. Ann. Statist. 14 (1986) 461-486
18. Berger J.O., and O'Hagan A. Ranges of posterior probabilities for unimodal priors with specified quantiles. In: Bernardo J.M., DeGroot M.H., Lindley D.V., and Smith A.F.M. (Eds). Bayesian Statistics, vol. 3 (1988), Oxford University Press, Oxford, UK
19. Berger J.O., Ríos Insua D., and Ruggeri F. Bayesian robustness. In: Ríos Insua D., and Ruggeri F. (Eds). Robust Bayesian Analysis (2000), Springer-Verlag, New York, USA
20. Betrò B., and Guglielmi A. Numerical robust Bayesian analysis under generalized moments conditions. In: Berger J.O., Betró B., Moreno E., Pericchi L.R., Ruggeri F., Salinetti G., and Wasserman L. (Eds). Bayesian Robustness (1996), Institute of Mathematical Statistics, Hayward, CA, USA
21. Betrò B., and Guglielmi A. Methods for global prior robustness under generalized moments conditions. In: Ríos Insua D., and Ruggeri F. (Eds). Robust Bayesian Analysis (2000), Springer-Verlag, New York, USA
22. Betrò B., and Ruggeri F. Conditional Gamma-minimax actions under convex losses. Comm. Statist. Theory Methods 21 (1992) 1051-1066
23. Betrò B., Mȩczarski M., and Ruggeri F. Robust Bayesian analysis under generalized moments conditions. J. Statist. Plann. Inference 41 (1994) 257-266
24. Boratynska A. On Bayesian robustness with the ε-contamination class of priors. Statist. Probab. Lett. 26 (1996) 323-328
25. Bose S. Bayesian robustness with mixture classes of priors. Ann. Statist. 22 (1994) 652-667
26. Box G.E.P., and Tiao G.C. A further look at robustness via Bayes theorem. Biometrika 49 (1962) 419-432 and 546
27. Box G.E.P., and Tiao G.C. Bayesian Inference in Statistical Analysis (1973), Addison-Wesley, New York, USA
28. Cagno E., Caron F., Mancini M., and Ruggeri F. Using AHP in determining prior distributions on gas pipeline failures in a robust Bayesian approach. Reliab. Engin. System Safety 67 (2000) 275-284
29. Cagno E., Caron F., Mancini M., and Ruggeri F. Sensitivity of replacement priorities for gas pipeline maintenance. In: Ríos Insua D., and Ruggeri F. (Eds). Robust Bayesian Analysis (2000), Springer-Verlag, New York, USA
30. Carota C., and Ruggeri F. Robust Bayesian analysis given priors on partition sets. Test 3 (1994) 73-86
31. Casella G., Hwang G., and Robert C. Loss functions for set estimation. In: Gupta S., and Berger J.O. (Eds). Statistical Decision Theory and Related Topics V (1994), Springer-Verlag, New York, USA
32. Chuang D.T. Further theory of stable decisions. In: Kadane J. (Ed). Robustness of Bayesian Analyses (1984), North-Holland, Amsterdam, The Netherlands
33. Cifarelli D.M., and Regazzini E. On a general definition of concentration function. Sankhyā, Ser. B 49 (1987) 307-319
34. Clarke B., and Gustafson P. On the overall sensitivity of the posterior distributions to its inputs. J. Statist. Plann. Inference 71 (1998) 137-150
35. Clyde M., and Chaloner K. The equivalence of constrained and weighted designs in multiple objective design problems. J. Amer. Statist. Assoc. 91 (1996) 1236-1244
36. Cuevas A., and Sanz P. On differentiability properties of Bayes operators. In: Bernardo J.M., DeGroot M.H., Lindley D.V., and Smith A.F.M. (Eds). Bayesian Statistics, vol. 3 (1988), Oxford University Press, Oxford, UK
37. DasGupta A., and Studden W.J. Frequentist behavior of robust Bayes estimates of normal means. Statist. Decisions 7 (1989) 333-361
38. De la Horra J., and Fernández C. Sensitivity to prior independence via Farlie-Gumbel-Morgenstern model. Comm. Statist. Theory Methods 24 (1995) 987-996
39. Dempster A.P. A subjectivist look at robustness. Bull. Internat. Statist. Inst. 46 (1975) 349-374
40. DeRobertis, L. (1978). The use of partial prior knowledge in Bayesian inference. Ph.D. Dissertation, Yale University, USA
41. DeRobertis L., and Hartigan J.A. Bayesian inference using intervals of measure. Ann. Statist. 1 (1981) 235-244
42. Dey D.K., and Birmiwal L.R. Robust Bayesian analysis using entropy and divergences measures. Statist. Probab. Lett. 20 (1994) 287-294
43. Dey D.K., Lou K., and Bose S. A Bayesian approach to loss robustness. Statist. Decisions 16 (1998) 65-87
44. Diaconis P., and Freedman D. On the consistency of Bayes estimates. Ann. Statist. 14 (1986) 1-67
45. Fortini S., and Ruggeri F. Concentration functions and Bayesian robustness. J. Statist. Plann. Inference 40 (1994) 205-220
46. Fortini S., and Ruggeri F. On defining neighbourhoods of measures through the concentration function. Sankhyā, Ser. A 56 (1994) 444-457
47. Fortini S., and Ruggeri F. Concentration function and sensitivity to the prior. J. Ital. Statist. Soc. 4 (1995) 283-297
48. Fortini S., and Ruggeri F. Differential properties of the concentration function. Sankhyā, Ser. A 59 (1997) 345-364
49. Fortini S., and Ruggeri F. On the use of the concentration function in Bayesian robustness. In: Ríos Insua D., and Ruggeri F. (Eds). Robust Bayesian Analysis (2000), Springer-Verlag, New York, USA
50. French S., and Ríos Insua D. Statistical Decision Theory (2000), Arnold
51. Gelfand A., and Dey D.K. On Bayesian robustness of contaminated classes of priors. Statist. Decisions 9 (1991) 63-80
52. Ghosh, S.K., Dey, D.K. (1994). Sensitivity diagnostics and robustness issues in Bayesian inference. Technical Report 94-30, Department of Mathematics, University of Connecticut, USA
53. Girón J., and Ríos S. Quasi-Bayesian behaviour: A more realistic approach to decision making?. In: Bernardo J.M., De Groot M.H., Lindley D.V., and Smith A.F.M. (Eds). Bayesian Statistics (1980), University Press, Valencia, Spain
54. Godsill S.J., and Rayner P.J.W. Robust treatment of impulsive noise in speech and audio signals. In: Berger J.O., Betró B., Moreno E., Pericchi L.R., Ruggeri F., Salinetti G., and Wasserman L. (Eds). Bayesian Robustness (1996), Institute of Mathematical Statistics, Hayward, CA, USA
55. Goldstein M. The linear Bayes regression estimator under weak assumptions. Biometrika 67 (1980) 621-628
56. Goutis C. Ranges of posterior measures for some classes of priors with specified moments. Internat. Statist. Rev. 62 (1994) 245-257
57. Greenhouse J., and Wasserman L. A practical robust method for Bayesian model selection: A case study in the analysis of clinical trials (with discussion). In: Berger J.O., Betró B., Moreno E., Pericchi L.R., Ruggeri F., Salinetti G., and Wasserman L. (Eds). Bayesian Robustness (1996), Institute of Mathematical Statistics, Hayward, CA, USA
58. Gustafson, P. (1994). Local sensitivity of posterior expectations. Ph.D. Dissertation, Department of Statistics, Carnegie Mellon University, USA
59. Gustafson P. Local sensitivity of posterior expectations. Ann. Statist. 24 (1996) 174-195
60. Gustafson P. Local robustness in Bayesian analysis. In: Ríos Insua D., and Ruggeri F. (Eds). Robust Bayesian Analysis (2000), Springer-Verlag, New York, USA
61. Gustafson P., and Wasserman L. Local sensitivity diagnostics for Bayesian inference. Ann. Statist. 23 (1995) 2153-2167
62. Hampel F.R., Ronchetti E.M., Rousseuw P.J., and Stahel W.A. Robust Statistics: The Approach Based on Influence Functions (1986), Wiley, New York, USA
63. Hartigan J.A. Linear Bayesian methods. J. Roy. Statist. Soc., Ser. B Stat. Methodol. 31 (1969) 446-454
64. Huber P.J. The use of Choquet capacities in statistics. Bull. Internat. Statist. Inst. 45 (1973) 181-191
65. Huber P.J. Robust Statistics (1981), Wiley, New York, USA
66. Hwang J.T. Universal domination and Stochastic domination: Estimation simultaneously under a broad class of loss functions. Ann. Statist. 13 (1985) 295-314
67. Kadane J., and Chuang D.T. Stable decision problems. Ann. Statist. 6 (1978) 1095-1110
68. Kadane J., and Srinivasan C. Discussion of Berger, J.O., An overview of robust Bayesian analysis (with discussion). Test 3 (1994) 93-95
69. Kadane J., and Srinivasan C. Bayesian robustness and stability (with discussion). In: Berger J.O., Betró B., Moreno E., Pericchi L.R., Ruggeri F., Salinetti G., and Wasserman L. (Eds). Bayesian Robustness (1996), Institute of Mathematical Statistics, Hayward, CA, USA
70. Kadane J., and Srinivasan C. Bayes decision problems and stability. Sankhyā, Ser. A 60 (1998) 383-404
71. Kadane J., Salinetti G., and Srinivasan C. Stability of Bayes decision and applications. In: Ríos Insua D., and Ruggeri F. (Eds). Robust Bayesian Analysis (2000), Springer-Verlag, New York, USA
72. Kass R., and Wasserman L. The selection of prior distributions by formal rules. J. Amer. Statist. Assoc. 91 (1996) 1343-1370
73. Lavine M. Sensitivity in Bayesian statistics: The prior and the likelihood. J. Amer. Statist. Assoc. 86 (1991) 396-399
74. Lavine M., Wasserman L., and Wolpert R.L. Bayesian inference with specified marginals. J. Amer. Statist. Assoc. 86 (1991) 400-403
75. Lavine M., Perone Pacifico M., Salinetti G., and Tardella L. Linearization techniques in Bayesian robustness. In: Ríos Insua D., and Ruggeri F. (Eds). Robust Bayesian Analysis (2000), Springer-Verlag, New York, USA
76. Madansky A. Bayesian analysis with incompletely specified prior distributions. In: Geisser S., et al. (Ed). Bayesian and Likelihood Methods in Statistics and Econometrics (1990), North-Holland, Amsterdam, The Netherlands
77. Makov U.E. Some aspects of Bayesian loss robustness. J. Statist. Plann. Inference 38 (1994) 359-370
78. Martín J., and Ríos Insua D. Local sensitivity analysis in Bayesian decision theory (with discussion). In: Berger J.O., Betró B., Moreno E., Pericchi L.R., Ruggeri F., Salinetti G., and Wasserman L. (Eds). Bayesian Robustness (1996), Institute of Mathematical Statistics, Hayward, CA, USA
79. Martín J., Ríos Insua D., and Ruggeri F. Issues in Bayesian loss robustness. Sankhyā Ser. A 60 (1998) 405-417
80. Martín J., Ríos Insua D., and Ruggeri F. Joint sensitivity in Bayesian decision theory. Test 12 (2003) 1-22
81. McCulloch R. Local model influence. J. Amer. Statist. Assoc. 84 (1989) 473-478
82. Moreno E., and Cano J.A. Robust Bayesian analysis for ε-contaminations partially known. J. Roy. Statist. Soc., Ser. B Stat. Methodol. 53 (1991) 143-155
83. Moreno E., and Cano J.A. Classes of bidimensional priors specified on a collection of sets: Bayesian robustness. J. Statist. Plann. Inference 46 (1992) 325-334
84. Moreno E., and Gonzalez A. Empirical Bayes analysis for ε-contaminated priors with shape and quantile constraints. Rebrape 4 (1990) 177-200
85. Moreno E., and Pericchi L.R. Bayesian robustness for ε-contaminations with shape and quantile constrains. Proc. Fifth Inter. Symp. on Applied Stochastic Models and Data Analysis (1991), World Scientific, Singapore
86. Moreno E., and Pericchi L.R. Bayesian robustness for hierarchical ε-contamination models. J. Statist. Plann. Inference 37 (1993) 159-168
87. Moreno E., Martínez C., and Cano J.A. Local robustness and influence for contamination classes of prior distributions (with discussion). In: Berger J.O., Betró B., Moreno E., Pericchi L.R., Ruggeri F., Salinetti G., and Wasserman L. (Eds). Bayesian Robustness (1996), Institute of Mathematical Statistics, Hayward, CA, USA
88. Nau, R. (1995). The shape of incomplete preferences. Technical Report, Duke University, USA
89. O'Hagan A., and Berger J.O. Ranges of posterior probabilities for quasi-unimodal priors with specified quantiles. J. Amer. Statist. Assoc. 83 (1988) 503-508
90. Parmigiani G. On optimal screening ages. J. Amer. Statist. Assoc. 88 (1993) 622-628
91. Peña D., and Zamar R.H. On Bayesian robustness: An asymptotic approach. In: Rieder H. (Ed). Robust Statistics, Data Analysis and Computer Intensive Methods (1996), Springer-Verlag, New York, USA
92. Pérez C., Martín J., and Müller P. Sensitivity analysis in medical decision problems. In: Prado, and Bolado (Eds). Proceedings SAMO 2001. second ed (2002), Editorial CIEMAT, Madrid 303-310
93. Pérez, C., Martín, J., Rufo, M.J. (2004). MCMC-based local parametric sensitivity. Technical Report, Department of Mathematics, Universidad de Extremadura, Spain
94. Philipps L.D. A theory of requisite decision models. Acta Psychologica 56 (1984) 29-48
95. Regazzini E. Concentration comparisons between probability measures. Sankhyā, Ser. B 54 (1992) 129-149
96. Ríos Insua D. Sensitivity Analysis in Multiobjective Decision Making (1990), Springer-Verlag, New York, USA
97. Ríos Insua D. On the foundations of decision making under partial information. Theory Decisions 33 (1991) 83-100
98. Ríos Insua D., and French S. A framework for sensitivity analysis in discrete multi-objective decision making. Eur. J. Oper. Res. 54 (1991) 176-190
99. Ríos Insua D., and Ruggeri F. Robust Bayesian Analysis (2000), Springer-Verlag, New York, USA
100. Ríos Insua D., Ruggeri F., and Vidakovic B. Some results on posterior regret Γ-minimax estimation. Statist. Decisions 13 (1995) 313-331
101. Ríos Insua S., Martín J., Ríos Insua D., and Ruggeri F. Bayesian forecasting for accident proneness evaluation. Scand. Actuar. J. 99 (1999) 134-156
102. Roberts A.W., and Varberg D.E. Convex Functions (1973), Academic Press, New York, USA
103. Ruggeri F. Posterior ranges of functions of parameters under priors with specified quantiles. Comm. Statist. Theory Methods 19 (1990) 127-144
104. Ruggeri, F. (1991). Infinitesimal sensitivity of likelihood function. Unpublished manuscript
105. Ruggeri, F. (2005). Gamma-minimax inference. Submitted for publication in: Balakrishnan, N., Read, C.B., Vidakovic, B. (Eds.), Encyclopedia of Statistical Sciences, second ed. Wiley, New York, USA
106. Ruggeri F., and Sivaganesan S. On a global sensitivity measure for Bayesian inference. Sankhyā, Ser. A 62 (2000) 110-127
107. Ruggeri, F., Wasserman, L. (1991). Density based classes of priors: Infinitesimal properties and approximations. Technical Report 528, Department of Statistics, Carnegie Mellon University, USA
108. Ruggeri F., and Wasserman L. Infinitesimal sensitivity of posterior distributions. Canad. J. Statist. 21 (1993) 195-203
109. Ruggeri F., and Wasserman L. Density based classes of priors: infinitesimal properties and approximations. J. Statist. Plann. Inference 46 (1995) 311-324
110. Ruggeri F., Martín J., and Ríos Insua D. Optimal alternative robustness in Bayesian decision theory. Rev. R. Acad. Cien. Serie A. Mat. 97 (2003) 407-412
111. Salinetti G. Stability of Bayesian decisions. J. Statist. Plann. Inference 40 (1994) 313-320
112. Saltelli A., Chan K., and Scott M. Sensitivity Analysis (2000), Wiley, New York, USA
113. Sargent D.J., and Carlin B.P. Robust Bayesian design and analysis of clinical trials via prior partitioning (with discussion). In: Berger J.O., Betró B., Moreno E., Pericchi L.R., Ruggeri F., Salinetti G., and Wasserman L. (Eds). Bayesian Robustness (1996), Institute of Mathematical Statistics, Hayward, CA, USA
114. Shao J. Monte Carlo approximations in Bayesian decision theory. J. Amer. Statist. Assoc. 84 (1989) 727-732
115. Shyamalkumar N.D. Likelihood robustness. In: Ríos Insua D., and Ruggeri F. (Eds). Robust Bayesian Analysis (2000), Springer-Verlag, New York, USA
116. Sivaganesan S. Sensitivity of some standard Bayesian estimates to prior uncertainty - a comparison. J. Statist. Plann. Inference 27 (1991) 85-103
117. Sivaganesan S. Robust Bayesian diagnostics. J. Statist. Plann. Inference 35 (1993) 171-188
118. Sivaganesan S. Global and local robustness approaches: Uses and limitations. In: Ríos Insua D., and Ruggeri F. (Eds). Robust Bayesian Analysis (2000), Springer-Verlag, New York, USA
119. Sivaganesan S., and Berger J.O. Ranges of posterior measures for priors with unimodal contaminations. Ann. Statist. 17 (1989) 868-889
120. Smith A.F.M., and Gelfand A.E. Bayesian statistics without tears: A sampling-resampling perspective. Amer. Statist. 46 (1992) 84-88
121. Varian H.R. A Bayesian approach to real state assessment. In: Fienberg S., and Zellner A. (Eds). Studies in Bayesian Econometrics and Statistics in Honor of L.J. Savage (1974), North-Holland, Amsterdam, The Netherlands
122. Vidakovic B. Γ-minimax: A paradigm for conservative robust Bayesians. In: Ríos Insua D., and Ruggeri F. (Eds). Robust Bayesian Analysis (2000), Springer-Verlag, New York, USA
123. Walley P. Statistical Reasoning With Imprecise Probabilities (1991), Chapman and Hall, London, UK
124. White D.J. Optimality and Efficiency (1982), Wiley, New York, USA
125. Yu P.L. Multiple Criteria Decision Making (1986), Plenum Press, New York, USA
126. Zen M.M., and DasGupta A. Estimating a binomial parameter: Is robust Bayes real Bayes?. Statist. Decisions 11 (1993) 37-60