BAYESIAN NONPARAMETRIC PREDICTIVE INFERENCE AND BOOTSTRAP TECHNIQUES

P. MULIERE AND P. SECCHI

Università di Pavia, Dipartimento di Economia Politica e Metodi Quantitativi, Via San Felice, 5, I-27100 Pavia, Italy

(Received January 23, 1995; revised January 5, 1996)

Abstract. We address the question as to whether a prior distribution on the space of distribution functions exists which generates the posterior produced by Efron’s and Rubin’s bootstrap techniques, emphasizing the connections with the Dirichlet process. We also introduce a new resampling plan which has two advantages: prior opinions are taken into account and the predictive distribution of the future observations is not forced to be concentrated on observed values.

Key words and phrases: Bootstrap techniques, Dirichlet process, nonparametric predictive inference.