Nonparametric Bayesian Estimation of Probability Densities by Function Space Techniques,

In the study the author considers the problem of estimating the density function which has given rise to a random sample. As opposed to the usual approaches which assume the functional form of the density function a priori, it is assumed that the density function is contained in a broad function class with mild continuity properties. The author then constructs prior measures on the function class and obtain the corresponding posterior measures given the random sample. The function space analogues of the posterior mean and the posterior mode are explored and their consistency properties investigated. Beyond the investigation of appropriate axioms which guarantee the nonparametric implementation of Bayes Theorem, it is shown how to use abstract Wiener measure to give an algorithmic technique for the use of Bayes Theorem in a function space setting. Modified author abstract