# Local Sensitivity Analysis using Divergence Measures under Weighted Distribution

• Chung, Younshik (Department of Statistics, Pusan National University) ;
• Dey, Dipak K. (Department of Statistics, University of Connecticut)
• Published : 2001.09.01

#### Abstract

This paper considers the use of local $\phi$-divergence measures between posterior distributions under classes of perturbations in order to investigate the inherent robustness of certain classes. The smaller value of the limiting local $\phi$-divergence implies more robustness for the prior or the likelihood. We consider the cases when the likelihood comes form the class of weighted distribution. Two kinds of perturbations are considered for the local sensitivity analysis. In addition, some numerical examples are considered which provide measures of robustness.

#### References

1. Bayesian analysis with distribution bands: the role of the loss function(Technical Report 208) Basu, S;Das Gupta, A
2. Annals of Statistics v.26 Robust Bayesian analysis of selection models Bayarri, M.J;Berger, J.O
3. Bayesian Statistics IV A BAD view of weighted distributions and selection models Bayarri, M.J;DeGroot, M;J.M. Bernardo(ed al., eds)
4. Robustness in Baysian Statistics The robust Bayesian viewpont (with discussion) Berger, J.O;J. Kadane(ed)
5. Statistical Decision Theory and Bayesian Analysis(2nd ed) Berger, J.O
6. Journal of Statistical Planning and Inference v.25 Robust Bayesian analysis sensitivity to the prior Berger, J.O
7. Proceedings of the Biophamaceatical section Semiparametric hierarchical selection models for Bayesian meta analysis Chung, Y;Dey, D.K;Jang, J
8. Studio Scientiarum Mathematicarum Hungarica v.2 Information-type measures of difference of probability distributions and indirect observations Csiszar, I
9. Journal of Statistical Planning and Inference v.40 Bayesian robustness for multiparameter problems Delampady, M;Dey, D.K
10. Statistics and Probability Letters v.20 Robust Bayesian analysis using entropy and divergence measures Dey, D.K;Birmiwal, L
11. IMS monograph series v.29 Bayesian Robustness: On local sensitivity measures in Bayesian analysis Dey, D.K;Ghosh, S.K;Lou, K.R;J.O. Berger(et al., eds)
12. Predictive inference: an introduction Geisser, S
13. Local sensitivity in Bayesian statistics Gustafson, P
14. Statistical Methods for Meta Analysis Hedges, L.V;Olkin, I
15. Statistical Sciences v.3 Selection models and the file drawer problem(with discussion) Iyenger, S;Greenhouse, J.B
16. Test v.5 Weighted distributions viewed in the context of model selection: a Bayesian perspective Larose, D;Dey, D.K
17. Classical and Contagious Discrete Distributions On discrete distributions arising out of methods of ascertainment Rao, C.R;G.P. Patil(ed.)
18. Goodness of fit statistics for discrete multivariate data Reid, T.R.C;Cressie, N.A.C
19. Canadian Journal of Statistics v.21 Infinitestimal sensitivity of posterior distributions Ruggeri, F;Wasserman, L
20. Biometrika v.84 Nonparametric classes of weighted functions to model publication bias Silliman, N.P
21. Journal of Statistical Planning and Inference v.35 Robust Bayesian diagnostics Sivaganesan, S