Model influence functions based on mixtures

Canadian Journal of Statistics

Volumn 24, Issue 4, 1996, Pages 535-548

  Gustafson, Paul ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Bayesian robustness; Influence function; Mixtures; Model sensitivity

Indexed keywords

EID: 0030336866     PISSN: 03195724     EISSN: None     Source Type: Journal    
DOI: 10.2307/3315332     Document Type: Article

References (21)

1. Andrews, D.F., Bickel, P.J., Hampel, F.R., Huber, P.J., Rogers, W.H., and Tukey, J.W. (1972). Robust Estimation of Location: Survey and Advances. Princeton University Press, Princeton.
2. Basu, S. (1994). Posterior sensitivity to the sampling distribution and the prior: more than one observation. Technical Report 66, Department of Mathematical Sciences, University of Arkansas.
3. Beitler, P.J., and Landis, J.R. (1985). A mixed-effects model for categorical data. Biometrics, 41, 991-1000.
4. Berger, J.O. (1994). An overview of robust Bayesian analysis (with discussion). Test, 3, 5-58.
5. Bose, S (1994). Bayesian robustness with mixture classes of priors. Ann. Statist., 22, 652-667.
6. Carlin, B.P., and Polson, N.G. (1992). Monte Carlo Bayesian methods for discrete regression models and categorical time series. Bayesian Statistics 4 (J.M. Bernardo, J.O. Berger, A.P. Dawid, and A.F.M. Smith, eds.), Oxford University Press, 577-586.
7. Carota, C., and Parmigiani, G. (1996). On Bayes factors for nonparametric alternatives. Bayesian Statistics 5 (J.M. Bernardo, J.O. Berger, A.P. Dawid, and A.F.M. Smith, eds.), Oxford University Press, 507-512.
8. Carota, C., Parmigiani, G., and Polson, N.G. (1996). Diagnostic measures for model criticism. J. Amer. Statist. Assoc., 91, 753-762.
9. Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J., and Stahel, W.A. (1986). Robust Statistics: The Approach Based on Influence Functions. Wiley, New York.
10. Huber, P.J. (1964). Robust estimation of a location parameter. Ann. Math. Statist., 35, 73-101.
11. Kadane, J.B., and Chuang, D.T. (1978). Stable decision problems. Ann. Statist., 6, 1095-1110.
12. Kadane, J.B., and Srinivasan, C. (1995). Bayes decision problems and stability. Preprint.
13. Kass, R.E., and Raftery, A.E. (1995). Bayes factors. J. Amer. Statist. Assoc., 90, 773-795.
14. Kass, R.E., Tierney, L., and Kadane, J.B. (1989). Approximate methods for assessing influence and sensitivity in Bayesian analysis. Biometrika, 76, 663-674.
15. Lavine, M. (1991). Sensitivity in Bayesian statistics: The prior and the likelihood. J. Amer. Statist. Assoc., 86, 396-399.
16. Lavine, M., Wasserman, L., and Wolpert, R. (1993). Linearization of Bayesian robustness problems. J. Statist. Plann. Inference, 37, 307-316.
17. Peng, F., and Dey, D.K. (1995). Bayesian analysis of outlier problems using divergence measures. Canad. J. Statist., 23, 199-213.
18. Ramsay, J.O., and Novick, M.R. (1980). PLU robust Bayesian decision theory: Point estimation. J. Amer. Statist. Assoc., 75, 901-907.
19. Srinivasan, C., and Truszczynska, H. (1990). On the ranges of posterior quantities. Technical Report 294, Department of Statistics, University of Kentucky.
20. Weiss, R.E. (1996). An approach to Bayesian sensitivity analysis. J. Roy. Statist. Soc. Ser. B. 58, 739-750.
21. Weiss, R.E., and Cook, D. (1992). A graphical case statistic for assessing posterior influence. Biometrika, 79, 51-55.