Numerical Bayesian Methods Applied to Signal Processing / Edition 1

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This book is concerned with the processing of signals that have been sampled and digitized. The authors present algorithms for the optimization, random simulation, and numerical integration of probability densities for applications of Bayesian inference to signal processing. In particular, methods are developed for the computation of marginal densities and evidence, and are applied to previously intractable problems either involving large numbers of parameters or where the signal model is of a complex form. The emphasis is on the applications of these methods notably to the restoration of digital audio recordings and biomedical data. After a chapter which sets out the main principles of Bayesian inference applied to signal processing, subsequent chapters cover numerical approaches to these techniques, the use of Markov chain Monte Carlo methods, the identification of abrupt changes in data using the Bayesian piecewise linear model, and identifying missing samples in digital audio signals.

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Product Details

  • ISBN-13: 9780387946290
  • Publisher: Springer New York
  • Publication date: 2/23/1996
  • Series: Statistics and Computing Series
  • Edition description: 1996
  • Edition number: 1
  • Pages: 244
  • Product dimensions: 0.69 (w) x 6.14 (h) x 9.21 (d)

Table of Contents

1 Introduction 1
2 Probabilistic Inference in Signal Processing 6
3 Numerical Bayesian Inference 26
4 Markov Chain Monte Carlo Methods 69
5 Retrospective Changepoint Detection 96
6 Restoration of Missing Samples in Digital Audio Signals 122
7 Integration in Bayesian Data Analysis 161
8 Conclusion 194
A The General Linear Model 201
B Sampling from a Multivariate Gaussian Density 207
C Hybrid Monte Carlo Derivations 209
D EM Algorithm Derivations 212
E Issues in Sampling Based Approaches to Integration 217
F Detailed Balance 223
References 227
Index 237
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