Bayesian influence analysis: A geometric approach

Biometrika

Volumn 98, Issue 2, 2011, Pages 307-323

  Zhu, Hongtu ^a   Ibrahim, Joseph G ^a   Tang, Niansheng ^b  

^a IL   (United States)

^b YUNNAN UNIVERSITY   (China)

Author keywords

Influence measure; Perturbation manifold; Perturbation model; Prior distribution

Indexed keywords

EID: 79957848736     PISSN: 00063444     EISSN: 14643510     Source Type: Journal    
DOI: 10.1093/biomet/asr009     Document Type: Review

References (37)

1. AMARI, S. (1990). Differential-Geometrical Methods in Statistics, 2nd edn. Lecture Notes in Statistics 28. Berlin: Springer.
2. BERGER, J. O. (1990). Robust Bayesian analysis: Sensitivity to the prior. J. Statist. Plan. Infer. 25, 303-28.
3. BERGER, J. O. (1994). An overview of robust Bayesian analysis. TEST 3, 5-58.
4. BERGER, J. O., RIOS INSUA, D. & RUGGERI, F. (2000). Bayesian robustness. Robust Bayesian Analysis, 1-32. In Lecture Notes in Statistics Eds D. Rios Insua and F. Ruggeri, 152. New York: Springer.
5. CARLIN, B. P. & POLSON, N. G. (1991). An expected utility approach to influence diagnostics. J. Am. Statist. Assoc. 86, 1013-22.
6. CHEN, M. H., SHAO, Q. M. & IBRAHIM, J. G. (2000) Monte Carlo Methods in Bayesian Computation. New York: Springer.
7. CLARKE, B. (2010). Desiderata for a predictive theory of statistics. Bayesian Anal. 5, 283-318.
8. CLARKE, B. & GUSTAFSON, P. (1998). On the overall sensitivity of the posterior distribution to its inputs. J. Statist. Plan. Infer. 71, 137-50. (Pubitemid 128340811)
9. COOK, R. D. (1986). Assessment of local influence (with Discussion) J. R. Statist. Soc. B. 48, 133-69.
10. COPAS, J. B. & EGUCHI, S. (2005). Local model uncertainty and incomplete-data bias (with discussion). J. R. Statist. Soc. B 67, 459-513. (Pubitemid 41351402)
11. DEY, D. K. & BIRMIWAL, L. R. (1994). Robust Bayesian analysis using divergence measures. Statist. Prob. Lett. 20, 287-94.
12. DEY, D. K.,GHOSH, S. K., & LOU, K. R. (1996). On local sensitivity measures in Bayesian analysis (with discussion). In Bayesian Robustness, J.O. Berger, B. Betro, E. Moreno, L. R. Pericchi, F. Ruggeri,G. Salinetti,&L. Wasserman, IMS Lecture Notes-Monograph Series, eds. 29, pp. 21-40 Hayward, CA.
13. DIJKSTRA, E. W. (1959). A note on two problems in connexion with graphs. Numer. Math. 1, 269-72.
14. EKELAND, I. (1978). The Hopf-Rinow theorem in infinite dimension. J. Diff. Geom. 13, 287-302.
15. ESCOBAR, M. D. (1994). Estimating normal means with a Dirichlet process prior. J. Am. Statist. Assoc. 89, 268-77.
16. FRIEDRICH, T. (1991). Die Fisher-Information und symplektische strukturen. Math. Nachr. 153, 273-96.
17. GUSTAFSON, P. (1996). Local sensitivity of inferences to prior marginals. J. Am. Statist. Assoc. 91, 774-82.
18. GUSTAFSON, P. (2000). Local robustness in Bayesian analysis. In D. Rios Insua and F. Ruggeri Robust Bayesian Analysis Eds. pp. 71-88 New York: Springer.
19. GUSTAFSON, P. & WASSERMAN, L. (1995). Local sensitivity diagnostics for Bayesian inference. Ann. Statist. 23, 2153-67.
20. GUTTMAN, I. & PE ÑA, D. (1993). A Bayesian look at diagnostics in the univariate linear model. Statist. Sinica 3, 367-90.
21. KASS, R. E. & RAFTERY, A. E. (1995). Bayes factors. J. Am. Statist. Assoc. 90, 773-95.
22. KASS, R. E., TIERNEY, L. & KADANE, J. B. (1989). Approximate methods for assessing influence and sensitivity in Bayesian analysis. Biometrika 76, 663-74.
23. KASS, R. E. & VOS, P. W. (1997). Geometrical Foundations of Asymptotic Inference. New York: Wiley.
24. LANG, S. (1995). Differential and Riemannian Manifolds, 3rd. ed. New York: Springer.
25. LAVINE, M. (1992). Local predictive influence in Bayesian linear models with conjugate priors. Commun. Statist. B 2, 269-83.
26. MCCULLOCH, R. E. (1989). Local model influence. J. Am. Statist. Assoc. 84, 473-78.
27. MILLAR, R. B. & STEWART, W. S. (2007). Assessment of locally influential observations in Bayesian models. Bayesian Anal. 2, 365-84.
28. OAKLEY, J. E. & O'HAGAN, A. (2004). Probabilistic sensitivity analysis of complex models: A Bayesian approach. J. R. Statist. Soc. B 66, 751-69. (Pubitemid 39015911)
29. PE ÑA, D. & GUTTMAN, I. (1993). Comparing probabilistic methods for outlier detection in linear models. Biometrika 80, 603-10.
30. PENG, F. & DEY, D. K. (1995). Bayesian analysis of outlier problems using divergence measures. Can. J. Statist. 23, 199-213.
31. RUGGERI, F. & SIVAGANESAN, S. (2000). On a global sensitivity measure for Bayesian inference. Sankhya 62, 110-27.
32. SIVAGANESAN, S. (2000). Global and local robustness approaches: Uses and limitations. In Robust Bayesian Analysis, Eds D. Rios Insua and F. Ruggeri. Lecture Notes in Statistics 152, pp. 89-108, New York: Springer.
33. VAN DER LINDE, A. (2007). Local influence on posterior distributions under multiplicative modes of perturbation. Bayesian Anal. 2, 319-32.
34. WANG, Q., STEFANSKI, L. A., GENTON, M. G. & BOOS, D. D. (2009). Robust time series analysis via measurement error modeling. Statist Sinica 19, 1263-80.
35. WU, X. & LUO, Z. (1993). Second-order approach to local influence. J. R. Statist. Soc. B 55, 929-36.
36. ZHU, H. T., IBRAHIM, J. G., LEE, S. Y. & ZHANG, H. P. (2007). Perturbation selection and influence measures in local influence analysis. Ann. Statist. 35, 2565-88.
37. ZHU, H. T. & LEE, S. Y. (2001). Local influence for incomplete data models. J. R. Statist. Soc. B 63, 111-26.