Bayesian Inference in Wavelet-Based Models by Peter Müller, Brani Vidakovic

By Peter Müller, Brani Vidakovic

This quantity offers an outline of Bayesian equipment for inference within the wavelet area. The papers during this quantity are divided into six elements: the 1st papers introduce uncomplicated options. Chapters partially II discover various methods to earlier modeling, utilizing autonomous priors. Papers within the half III speak about determination theoretic elements of such past versions. partly IV, a few features of previous modeling utilizing priors that account for dependence are explored. half V considers using 2-dimensional wavelet decomposition in spatial modeling. Chapters partially VI talk about using empirical Bayes estimation in wavelet dependent types. half VII concludes the amount with a dialogue of case stories utilizing wavelet dependent Bayesian methods. The cooperation of all participants within the well timed coaching in their manuscripts is drastically well-known. We determined early on that it was once impor­ tant to referee and seriously assessment the papers which have been submitted for inclusion during this quantity. For this large activity, we trusted the carrier of diverse referees to whom we're such a lot indebted. we're additionally thankful to John Kimmel and the Springer-Verlag referees for contemplating our suggestion in a truly well timed demeanour. Our distinct thank you visit our spouses, Gautami and Draga, for his or her support.

Show description

Read or Download Bayesian Inference in Wavelet-Based Models PDF

Best mathematical analysis books

Understanding Digital Signal Processing, Second Edition

The consequences of DSP has entered each part of our lives, from making a song greeting playing cards to CD avid gamers and cellphones to clinical x-ray research. with out DSP, there will be no web. lately, each element of engineering and technology has been prompted via DSP as a result of ubiquitous laptop laptop and available sign processing software program.

A Formal Background to Mathematics: Logic, Sets and Numbers

§1 confronted by means of the questions pointed out within the Preface i used to be triggered to put in writing this e-book at the assumption regular reader can have yes features. he'll most likely be accustomed to traditional money owed of yes parts of arithmetic and with many so-called mathematical statements, a few of which (the theorems) he'll recognize (either simply because he has himself studied and digested an evidence or simply because he accepts the authority of others) to be real, and others of which he'll comprehend (by a similar token) to be fake.

Wavelet Neural Networks With Applications in Financial Engineering, Chaos, and Classification

Via broad examples and case studies, Wavelet Neural Networks provides a step by step creation to modeling, education, and forecasting utilizing wavelet networks. The acclaimed authors current a statistical version identity framework to effectively follow wavelet networks in a number of functions, in particular, offering the mathematical and statistical framework wanted for version choice, variable choice, wavelet community building, initialization, education, forecasting and prediction, self assurance periods, prediction periods, and version adequacy trying out.

Additional info for Bayesian Inference in Wavelet-Based Models

Sample text

References Benedetto, J. J. and Frazier, M. W. (1994) Wavelets: Mathematics and Applications, CRC Press, Bocan Raton, Florida. Bloomfield, P. (1976) Fourier analysis of time series, an introduction, Wiley, New York. Daubechies, I. (1992) Ten Lectures on Wavelets,. SIAM, Philadelphia. Donoho, D. L. and Johnstone, I. M. (1995). Adapting to unknown smoothness via Wavelet shrinkage, J. Amer. Statist. , 90, 1200-1224. 32 Marron Donoho, D. , Johnstone, I. , Kerkyacharian, G. and Picard, D. (1995). Wavelet shrinkage: Asymptopia?

Note that using this basis, the signal recovery is excellent for both of these data sets. In contrast, the Fourier basis gave excellent recovery of the smooth sinusoidal target, but very poor performance for the step target, while the Haar basis gave excellent recovery of the step target, but poor recovery of the sinusoidal target. The key to understanding this is "signal compression" . The Fourier basis represents the sinusoid with very few coefficients, but needs many for the step. The Haar represents the step with few coefficients, but needs many for the sinusoid.

Overcomplete wavelet dictionaries are obtained by sampling indices more finely. An important example of overcomplete wavelet dictionaries is the non-decimated (or stationary or translation-invariant) wavelet dictionary (see, for example, Coifman & Donoho, 1995; Nason & Silverman, 1995). Atomic decompositions in overcomplete dictionaries are obviously nonunique and one may think about choosing the 'best' possible representation among many available (see, for example, Mallat & Zhang, 1993; Davis, Mallat & Zhang, 1994; Chen, Donoho & Saunders, 1999).

Download PDF sample

Rated 4.98 of 5 – based on 38 votes