Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6858924 | International Journal of Approximate Reasoning | 2016 | 15 Pages |
Abstract
Posterior and predictive distributions for m future trials, given the first n elements of an infinite exchangeable sequence ξË1,ξË2,â¦, are considered in a nonparametric Bayesian setting. The former distribution is compared to the unit mass at the empirical distribution eËn:=1nâi=1nδξËi of the n past observations, while the latter is compared to the m-fold product eËnm. Comparisons are made by means of distinguished probability distances inducing topologies that are equivalent to (or finer than) the topology of weak convergence of probability measures. After stating almost sure convergence to zero of these distances as n goes to infinity, the paper focuses on the analysis of the rate of approach to zero, so providing a quantitative evaluation of the approximation of posterior and predictive distributions through their frequentistic counterparts δeËn and eËnm, respectively. Characteristic features of the present work, with respect to more common literature on Bayesian consistency, are: first, comparisons are made between entities which depend on the n past observation only; second, the approximations are studied under the actual (exchangeable) law of the ξËn's, and not under hypothetical product laws p0â, as p0 varies among the admissible determinations of a random probability measure.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Artificial Intelligence
Authors
Donato Michele Cifarelli, Emanuele Dolera, Eugenio Regazzini,