Colloquium
The Department of Statistics

presents

Brani Vidakovic
Duke University

Bayesian Wavelet Shrinkage and Applications in
Time Series and Turbulence Measurements

Abstract

I will introduce and discuss the paradigm of Bayesian wavelet shrinkage and give a few examples at the beginning of the talk. The main body of the talk is concerned with two applications in time series. The first application deals with estimating a spectral density by Bayesianly induced shrinkage of periodograms in the wavelet domain. Some theoretical results and examples are provided. The second application is concerned denoising of turbulence measurements. Bayesian filtering of ozone O_3 time series takes into account whitening properties of wavelet transforms and robust behavior of the second order statistics, as stipulated by the celebrated Kolmogorov's K41 law.