Multivariate Bayesian Statistics
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Multivariate Bayesian Statistics : Models for Source Separation and Signal Unmixing

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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.show more

Product details

  • Hardback | 352 pages
  • 161 x 246.9 x 23.9mm | 657.72g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • New.
  • 19 black & white illustrations, 46 black & white tables
  • 1584883189
  • 9781584883180

Review quote

"This book is a thorough exposition of Bayesian modeling techniques. Overall, the book is well written and gives a detailed step-by-step approach to some widely applicable model types. This book helps me understand how to build some complex models using a Bayesian approach with a much better understanding of what effect my decisions will have on the final model results." - Technometrics, Feb. 2005, Vol. 47, No. 1 "A very useful and valuable book on a topic of great importance for researchers and students with interest in Bayesian techniques. Summing Up: Highly recommended." -D.V. Chopra in CHOICE, June 2003show more

Table of contents

Introduction Part l: FUNDAMENTALS STATISTICAL DISTRIBUTIONS Scalar Distributions Vector Distributions Matrix Distributions INTRODUCTORY BAYESIAN STATISTICS Discrete Scalar Variables Continuous Scalar Variables Continuous Vector Variables Continuous Matrix Variables PRIOR DISTRIBUTIONS Vague Priors Conjugate Priors Generaliz ed Priors Correlation Priors HYPERPARAMETER ASSESSMENT Introduction Binomial Likelihood Scalar Normal Likelihood Multivariate Normal Likelihood Matrix Normal Likelihood BAYESIAN ESTIMATION METHODS Marginal Posterior Mean Maximum a Posteriori Advantages of ICM over Gibbs Sampling Advantages of Gibbs Sampling over ICM REGRESSION Introduction Normal Samples Simple Linear Regression Multiple Linear Regression Multivariate Linear Regression Part II: II Models BAYESIAN REGRESSION Introduction The Bayesian Regression Model Likelihood Conjugate Priors and Posterior Conjugate Estimation and Inference Generalized Priors and Posterior Generalized Estimation and Inference Interpretation Discussion BAYESIAN FACTOR ANALYSIS Introduction The Bayesian Factor Analysis Model Likelihood Conjugate Priors and Posterior Conjugate Estimation and Inference Generalized Priors and Posterior Generalized Estimation and Inference Interpretation Discussion BAYESIAN SOURCE SEPARATION Introduction Source Separation Model Source Separation Likelihood Conjugate Priors and Posterior Conjugate Estimation and Inference Generalized Priors and Posterior Generalized Estimation and Inference Interpretation Discussion UNOBSERVABLE AND OBSERVABLE SOURCE SEPARATION Introduction Model Likelihood Conjugate Priors and Posterior Conjugate Estimation and Inference Generalized Priors and Posterior Generalized Estimation and Inference Interpretation Discussion 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 Introduction Model Delayed Constant Mixing Delayed Nonconstant Mixing Instantaneous Nonconstant Mixing Likelihood Conjugate Priors and Posterior Conjugate Estimation and Inference Generalized Priors and Posterior Generalized Estimation and Inference Interpretation Discussion CORRELATED OBSERVATION AND SOURCE VECTORS Introduction Model Likelihood Conjugate Priors and Posterior Conjugate Estimation and Inference Posterior Conditionals Generalized Priors and Posterior Generalized Estimation and Inference Interpretation Discussion CONCLUSION Appendix A FMRI Activation Determination Appendix B FMRI Hyperparameter Assessment Bibliography Indexshow more

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