Statistical models for data that scale: multiscale domain summaries with applications to geophysical data, high frequency biometric responses and medical images

Abstract

The theory of wavelets and Multiscale analysis motivate a large proportion of modern statistical methodology and advances in non-statistical fields have led to important, even indispensable statistical tools. Massive data sets, functional data, and high-frequency sampled processes intrinsically invariant to changes in scale are increasingly observed and stored. As a result, it is often claimed that "scaling is omnipresent". General multiscale domains provide an environment for analyzing and modeling such processes, and for unifying several related phenomena including fractality, multi-fractality, self-similarity, and long range dependence. The success of wavelets in particular is attributed to their low computational complexity, good locality and adaptivity, decorrelation property, good filtering capability, ability to assess the scaling in the data, and aptness to incorporate prior information about the phenomenon. We are going to work on Scale-Mixing Transform and Scale-Mixing Wavelet Spectra and present examples from several areas where these proposed methodology may be applied and tested. (AU)