**Sankhya: The Indian Journal of Statistics**

1996, Volume 58, Series A, Pt. 2, pp. 283--291

**EXPLORING A BAYESIAN FOLKLORE : POSTERIOR IS SEQUENTIALLY UPDATED PRIOR**

By

SUMAN MAJUMDAR, *University of Connecticut*

SUMMARY. It is well entrenched in Byesian folklore that the posterior distribution when the sample size $n(\geq 1)$ is independent (given the sampling distribution) and identically distributed equals the posteriors distribution when the sample is sequentially drawn with the prior updated at every stage. This is vacuously true for a parameterized dominated statistical experiment when the prior is specified through a density ( via telescopic cancellation of normalizing constants). This equality is explored here when the experiment is neither parameterized nor dominated the prior is not specified through a density, and the sample may be the subject to censoring. It turns out that the equality holds under what LeCam (1986) calls the Polish assumption (cf. p.326). The result validates the two-stage computation of the Bayes estimator of the Survival Function in Susarla and Van Ryzin (1976).

*AMS (1991) subject classification.* Primary 62C10, secondary 60A10.

*Key words and phrases.* Atom, determining class, regular conditional distribution.