Multivariate Bayesian Statistics

Daniel B. Rowe

350 pages, parution le 24/12/2002

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Résumé

Offers the first Bayesian approach to the source separation problem
Provides all of the mathematical and statistical background needed, from statistical distributions and introductory Bayesian probability to prior hyperparameter assessment and estimation methods
Covers the multivariate regression model, the factor analysis model, the Bayesian Source Separation model, the unobservable and observable source separation model, the delayed source separation model, the dynamic mixing coefficient models, and the correlation model, all discussed from the Bayesian perspective

Of the two primary approaches to the classic source separation problem, only one does not impose potentially unreasonable model and likelihood constraints: the Bayesian statistical approach. Bayesian methods incorporate the available information regarding the model parameters and not only allow estimation of the sources and mixing coefficients, but also allow inferences to be drawn from them.

Multivariate Bayesian Statistics: Models for Source Separation and Signal Unmixing offers a thorough, self-contained treatment of the source separation problem. After an introduction to the problem using the "cocktail-party" analogy, Part I provides the statistical background needed for the Bayesian source separation model. Part II considers the instantaneous constant mixing models, where the observed vectors and unobserved sources are independent over time but allowed to be dependent within each vector. Part III details more general models in which sources can be delayed, mixing coefficients can change over time, and observation and source vectors can be correlated over time. For each model discussed, the author gives two distinct ways to estimate the parameters.

Real-world source separation problems, encountered in disciplines from engineering and computer science to economics and image processing, are more difficult than they appear. This book furnishes the fundamental statistical material and up-to-date research results that enable readers to understand and apply Bayesian methods to help solve the many "cocktail party" problems they may confront in practice.

Contents

Part l: Fundamentals

Statistical Distributions
Introductory Bayesian Statistics
Prior Distributions
Hyperparameter Assessment
Bayesian Estimation Methods
Regression

Part II: II Models

Bayesian regression
Bayesian Factor Analysis
Bayesian Source Separation
Unobservable And Observable Source Separation
FMRI Case Study
Introduction
Model
Priors and Posterior
Estimation and Inference
Simulated FMRI Experiment
Real FMRI Experiment
FMRI Conclusion

Part III: Generalizations

Delayed Sources And Dynamic Coefficients
Correlated Observation And Source Vectors
Conclusion

Appendix A FMRI Activation Determination
Appendix B FMRI Hyperparameter Assessment

L'auteur - Daniel B. Rowe

Medical College of Wisconsin, Wisconsin, USA

Caractéristiques techniques

	PAPIER
Éditeur(s)	Chapman and Hall / CRC
Auteur(s)	Daniel B. Rowe
Parution	24/12/2002
Nb. de pages	350
Format	16 x 24
Couverture	Relié
Poids	661g
Intérieur	Noir et Blanc
EAN13	9781584883180
ISBN13	978-1-58488-318-0