Sankhya: The Indian Journal of Statistics

1997, Volume 59, Series A, Pt. 3, 376-391

**MEASURING THE EFFECT OF OBSERVAIONS USING THE POSTERIOR AND THE INTRINSIC BAYES FACTORS WITH VAGUE PRIOR INFORMATION**

By

DIPAK K. DEY, *University of Connecticut, Storrs*

SUJIT K. GHOSH, *North Carolina State University, Raleigh *

And

HONG CHANG, *Coopers & Lybrand L.L.P., Boston *

SUMMARY. Model determination is one of the fundamental problems in statistics. In this paper we consider model selection amongst a finite set of models along with model adequacy which are two integrated parts of model determination. We consider a measure of the effect of the individual observations on the posterior and the intrinsic Bayes factors by studying the change in it after deleting an observation. The results are extremely useful in those applications where we consider a vague prior information. Several standard examples are provided where the measure can be expressed in closed form. Nonstandard examples which include nonlinear models and double exponential models are considered where sampling based methods are utilized to carry out required computations.

*AMS (1991) subject classification.* 62F15, 62C10

*Key words and phrases*. Bayes factor, double exponential model, influential observation, intrinsic Bayes factor, Jefferys' prior, Laplace method, noninformative prior, posterior Bayes factor