Traditional Bayesian inference has followed the paradigm of expressing information and degree of uncertainty about the information prior to the gathering of data, and then reexpressing the collective information and subsequent degree of uncertainty after incorporating the data. Much of the Bayesian research on a wide variety of statistical issues has used parametrized functions in this paradigm. The extension of statistical theory and methodology to broader classes of functions, or even to procedures, which are no longer simply characterized by small numbers of parameters, requires extension of this Bayesian paradigm. This research addresses several specific extensions of this kind: monotone densities and monotone hazard rates and their extension to spherical distributions, bootstrap procedures, and infinite-dimensional parametric problems.
