Rates of convergence of Bayesian nonparametric procedures are expressed as the maximum between two rates: one is determined via suitable measures of concentration of the prior around the “true” density f0, and the other is related to the way the mass is spread outside a neighborhood of f0. Here we provide a lower bound for the former in terms of the usual notion of prior concentration and in terms of an alternative definition of prior concentration. Moreover, we determine the latter for two important classes of priors: the infinite–dimensional exponential family, and the Polya trees.
On convergence rates for nonparametric posterior distributions
PRUENSTER, Igor;
2007-01-01
Abstract
Rates of convergence of Bayesian nonparametric procedures are expressed as the maximum between two rates: one is determined via suitable measures of concentration of the prior around the “true” density f0, and the other is related to the way the mass is spread outside a neighborhood of f0. Here we provide a lower bound for the former in terms of the usual notion of prior concentration and in terms of an alternative definition of prior concentration. Moreover, we determine the latter for two important classes of priors: the infinite–dimensional exponential family, and the Polya trees.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
