Bayesian False Discovery Rate Wavelet Shrinkage: Theory and Applications

The interest in inference in the wavelet domain remains vibrant area of statistical research because of needs of scientific community to process and explore massive data sets. Prime examples are geophysical, biomedical, and internet related data. In this paper we develop wavelet shrinkage methodology based on testing multiple hypotheses in the wavelet domain. This approach had been considered by many researchers and goes back to the early 1990's. Even the early proposal, the universal thresholding, could be interpreted as a test of multiple hypotheses in the wavelet domain. We propose two new approaches to wavelet shrinkage. (i) In the spirit of Efron's work on local false discovery rate, we propose the theoretical counterpart Bayesian Local False Discovery Rate, BLFDR, where the underlying model assumes unknown variances. This approach to wavelet shrinkage can be connected with shrinkage based on Bayes factors. (ii) The second proposal to wavelet shrinkage explored in this p...

• Type: Journal
• Year: 2008
• Where: CSSC
• Authors: Ilya Lavrik, Yoon Young Jung, Fabrizio Ruggeri, Brani Vidakovic
• Keywords: CSSC 2008, False Discovery Rate, Wavelet, Wavelet Domain