Department of Statistical Science

Duke University

presents:

Pietro Muliere

Universita di Pavia

"Predictive Inference and Bootstrap Techniques"

Abstract:

Let {Xn} be an exchangeable sequence of real random variables (r.v.) defined on a probability space (OMEGA, F, P). Assume that the r.v. {Xn} are independent and identically distributed given the random variable.

The first aim of this talk is to discuss if it is reasonable to approximate the posterior distribution L(LAMBDA|X1....,Xn) by means of the bootstrap procedure applied to a statistic Tn(X1, ...,Xn) "sufficient for predictive purposes" when the researcher is not able to synthesize opinions about through the specification of a prior distribution.

Secondarily, I address the question of whether a prior distribution on the space of distribution functions exists which generates the posterior produced by Efron's and Rubin's bootstraps, emphasizing the connections with the Dirichlet process.

Finally I introduce a new bayesian re-sampling plan, showing that the random probability distribution which supports this re-sampling plan approximates, in the sense of weak convergence, the Dirichlet process.

Friday, November 3, 1995

11:45 - 12:45

116 Old Chemistry Building

Any questions concerning the seminar may be addressed to Cheryl McGhee @ (919) 684-8029, e-mail cheryl@stat.duke.edu, or finger seminar@stat.duke.edu.