The prior distribution of a random measure

Nguyen Bac-Van¹

¹ Department of Statistics VNUHCM-University of Science 227 Nguyen-Van-Cu Q5 Ho Chi Minh City, Vietnam

Applicationes Mathematicae, Tome 46 (2019) no. 1, pp. 39-52

Résumé

It is known that an infinite, exchangeable sequence of observations from a Borel space, in particular a Polish one, is underlain by an almost surely (a.s.) unique random probability measure on this space such that, conditioned on it, the observations are independent and identically distributed with that measure. The distribution of that random measure is the prior distribution involved in Bayes inference. The present paper proves that the prior distribution of the a.s. unique random measure underlying an infinite, exchangeable sequence of observations from a Polish space is a Radon probability measure on the $\sigma $-field generated by the narrow topology in the space of Borel probability measures on the starting Polish space.

Détail

DOI : 10.4064/am2362-7-2018

Keywords: known infinite exchangeable sequence observations borel space particular polish underlain almost surely unique random probability measure space conditioned observations independent identically distributed measure distribution random measure prior distribution involved bayes inference present paper proves prior distribution unique random measure underlying infinite exchangeable sequence observations polish space radon probability measure sigma field generated narrow topology space borel probability measures starting polish space