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Abstract:
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We describe a Bayesian approach for curve estimation based on an overcomplete wavelet dictionary proposed by Abramovich, Sapatinas and Silverman (1999), where the function is modeled by a sum of the wavelet components at arbitrary locations and scales, on which prior distributions are imposed. We believe that by avoiding the dyadic constraints for orthonormal wavelet bases, the overcomplete wavelet dictionary will have greater flexibility to match the structure of the data, and give sparser representations. The main challenge here is to efficiently search over an infinite number of basis elements. We will discuss a reversible jump Markov Chain Monte Carlo algorithm for inference on the parameters, and strategies to give better convergence. We will also present simulation results using standard test functions, which show that the new method leads to greater sparsity and improved MSE.
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