Multiscale statistical models

We present an overview of recent efforts developing a framework for a new class of statistical models based on the concept of multiscale likelihood factorizations. This framework blends elements of wavelets, recursive partitioning, and graphical models to derive a probabilistic analogue of an orthogonal wavelet decomposition. The casting of these results within a likelihood-based context allows for the extension of certain key properties of classical wavelet based estimators to a setting that includes, within a single unified perspective, models for continuous, count, and categorical datatypes.