Bayesian Nonparametric Bootstrap Confidence Intervals

Abstract : Let X sub 1,...,X sub n be a random sample from an unknown probability distribution P on the sample space X, and let theta = theta(P) be a parameter of interest. This paper gives a Bayesian botstrap method of obtaining Bayes estimates and Bayesian confidence limits for theta, using a (non- degenerate) Dirichlet process prior for P. This extends methods and results of Rubin (1981) and Efron (1982), in that they assume the sample space to be finite and use only a particular degenerate Dirichlet prior. An asymptotic justification of the Bayesian bootstrap is given, parallelling results of Bickel and Freedman(1981). Keywords: Charts; Approximation(mathematics); Asymptotic theory.