Bayesian marginal influence assessment

Journal of Statistical Planning and Inference

Volumn 71, Issue 1-2, 1998, Pages 163-177

  Weiss, Robert E ^a   Cho, Meehyung ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Gibbs sampler; Kullback divergence* L1 norm; Longitudinal data; Nested Gibbs sampler; Random effects model; 2 divergence

Indexed keywords

EID: 0040092426     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0378-3758(98)00015-9     Document Type: Article

References (26)

1. Atkinson, B.W., 1986. Plots, Transformations, and Regression: An Introduction to Graphical Methods of Diagnostic Regression Analysis. Clarendon Press, Oxford.
2. Belsley, D.A., Kuh, E., Welsch, R.E., 1980. Regression Diagnostics. Wiley, New York.
3. Bernardo J.M. Expected information as expected utility. Ann. Statist. 7:1979;686-690.
4. Bernardo, J.M., 1985. Discussion of Pettit and Smith 1985 In: Bernardo, J.M., DeGroot, M.H., Lindley, D.V., Smith, A.F.M., (Eds.), Bayesian Statist. 2. North-Holland, Amsterdam, pp. 492-493.
5. Bradlow, E., Zaslavsky, A., 1997. Case influence analysis in Bayesian inference. J. Comp. Graph. Statist. 6, 214-331.
6. Carlin B.P., Polson N.G. An expected utility approach to influence diagnostics. J. Amer. Statist. Assoc. 86:1991;1013-1021.
7. Chatterjee, S., Hadi, A.S., 1988. Sensitivity Analysis in Linear Regression. Wiley, New York.
8. Cook, R.D., Weisberg, S., 1982. Residuals and Influence in Regression. Chapman & Hall, New York.
9. De Gruttola, V., Ware, J.H., Louis, T.A., 1987. Influence analysis of generalized least squares estimators. J. Amer. Statist. Assoc. 82 911-917.
10. Fanurik D., Zeltzer L.K., Roberts M.C., Blount R.L. The relationship between children's coping styles and psychological interventions for cold pressor pain. Pain. 53:1993;213-222.
11. Geisser, S., 1993. Predictive Inference, An Introduction. Chapman & Hall, New York.
12. Gelfand A.E., Smith A.F.M. Sampling-based approaches to calculating marginal densities. J. Amer. Statist. Assoc. 85:1990;398-409.
13. Guttman, I., Peña, D., 1988. Outliers and influence: Evaluation by posteriors of parameters in the linear model. In: Bernardo, J.M., DeGroot, M.H., Lindley, D.V., Smith, A.F.M., (Eds.), Bayesian Statist. 3. Oxford University Press, Oxford, 631-640.
14. Hobert J.P., Casella G. The effect of improper priors on Gibbs sampling in hierarchical linear mixed models. J. Amer. Statist. Assoc. 91:1996;1461-1473.
15. Johnson W. Influence measures for logistic regression: another point of view. Biometrika. 72:1985;59-65.
16. Johnson, W., Geisser S., 1982. Assessing the predictive influence of observations. Statistics and Probability: Essays in Honor of C.R. Rao. North-Holland, Amsterdam, 343-358.
17. Johnson W., Geisser S. A predictive view of the detection and characterization of influential observations in regression analysis. J. Amer. Statist. Assoc. 78:1983;137-144.
18. Johnson W., Geisser S. Estimative influence measures for the multivariate general linear model. J. Statist. Plann. Inference. 11:1985;33-56.
19. Kass R.E., Tierney L., Kadane J. Approximate methods for assessing influence and sensitivity in Bayesian analysis. Biometrika. 76:1989;663-674.
20. Mickey M.R., Dunn O.J., Clark V. Note on the use of stepwise regression in detecting outliers. Comput. in Biomed. Res. 1:1967;105-109.
21. Pettit L.I. The conditional predictive ordinate for the normal distribution. J. Roy. Statist. Soc. Ser. B 52:1990;175-184.
22. Pettit, L.I., Smith, A.F.M., 1985. Outliers and influential observations in linear models. In: Bernardo, J.M., Degroot, M., Lindly, D., Smith, A.F.M., (Eds.), Bayesian Statist. 2. North Holland, Amsterdam, 473-494.
23. Smith A.F.M., Roberts G.O. Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods. J. Roy. Statist. Soc. Ser. B 55:1993;53-102.
24. Weiss, R.E., 1996a. An approach to Bayesian sensitivity analysis. J. Roy. Statist. Soc. Ser B, 58, 739-750.
25. Weiss, R.E., 1996b. Sufficiency and influence. In: Bayesian Robustness, IMS Lecture Notes - Monograph Series, vol. 29, (Eds.) Berger, J.O., Betco, B., Moreno, E., Pericchi, L.R., Ruggeri, F., Salinetti, G., Wasserman, L., In: IMS, Hayward, CA, 213-228.
26. Weiss R.E., Wang Y., Ibrahim J. Predictive model selection for repeated measures random effects models using Bayes factors. Biometrics, 53:1997;159-169.