Bayesian False Discovery Rate Wavelet Shrinkage: Theory and Applications |
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| Authors: | Ilya Lavrik Yoon Young Jung Brani Vidakovic |
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| Affiliation: | 1. Department of Biomedical Engineering , Georgia Institute of Technology , Atlanta, Georgia, USA;2. Department of Biomedical Engineering , Georgia Institute of Technology , Atlanta, Georgia, USA;3. Department of Statistics , Ewha Womans University , Seoul, Korea |
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| Abstract: | Statistical inference in the wavelet domain remains a vibrant area of contemporary statistical research because of desirable properties of wavelet representations and the need of scientific community to process, explore, and summarize massive data sets. Prime examples are biomedical, geophysical, and internet related data. We propose two new approaches to wavelet shrinkage/thresholding. In the spirit of Efron and Tibshirani's recent work on local false discovery rate, we propose Bayesian Local False Discovery Rate (BLFDR), where the underlying model on wavelet coefficients does not assume known variances. This approach to wavelet shrinkage is shown to be connected with shrinkage based on Bayes factors. The second proposal, Bayesian False Discovery Rate (BaFDR), is based on ordering of posterior probabilities of hypotheses on true wavelets coefficients being null, in Bayesian testing of multiple hypotheses. We demonstrate that both approaches result in competitive shrinkage methods by contrasting them to some popular shrinkage techniques. |
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| Keywords: | Bayesian local false discovery rate False discovery rate Multiple hypothesis testing Shrinkage |
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