Multivariate Density Estimation and Its Applications

Abstract

In this talk we will report recent progress on multivariate density estimation. Our approach is based on the construction of priors on the space of simple functions. The key challenge is to learn the partition that support the simple function. We will present methods for doing this when the dimension is in the range of 4 to 50. The ability to estimate multivariate densities effectively will enable the development of new methods in other areas of statistics. We will illustrate this with examples from the areas of prediction and data compression. ?