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收藏 2010-06-11

Multivariate Bayesian Statistics: Models for Source Separation and Signal Unmixing [Hardcover]
Daniel B. Rowe (Author)

Editorial Reviews

Review

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

Product Description

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.

Product Details

Hardcover: 352 pages
Publisher: Chapman and Hall/CRC; 1 edition (November 25, 2002)
Language: English
ISBN-10: 1584883189
ISBN-13: 978-1584883180

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kxjs2007

2010-6-11 07:58:46

Contents
List of Figures
List of Tables
1 Introduction
1.1 The Cocktail Party
1.2 The Source Separation Model
I Fundamentals
2 Statistical Distributions
2.1 Scalar Distributions
2.1.1 Binomial
2.1.2 Beta
2.1.3 Normal
2.1.4 Gamma and Scalar Wishart
2.1.5 Inverted Gamma and Scalar Inverted Wishart
2.1.6 Student t
2.1.7 F-Distribution
2.2 Vector Distributions
2.2.1 Multivariate Normal
2.2.2 Multivariate Student t
2.3 Matrix Distributions
2.3.1 MatrLx Normal
2.3.2 Wishart
2.3.3 Inverted Wishart
2.3.4 MatrLx T
3 Introductory Bayesian Statistics
3.1 Discrete Scalar Variables
3.1.1 Bayes' Rule and Two Simple Events
3.1.2 Bayes' Rule and the Law of Total Probability
3.2 Continuous Scalar Variables
3.3 Continuous Vector Variables
3.4 Continuous Matrix Variables
4 Prior Distributions
4.1 Vague Priors
4.1.1 Scalar Variates
4.1.2 Vector Variates
4.1.3 Mat rLx Variates
4.2 Conjugate Priors
4.2.1 Scalar Variates
4.2.2 Vector Variates
4.2.3 Mat rLx Variates
4.3 Generalized Priors
4.3.1 Scalar Variates
4.3.2 Vector Variates
4.3.3 Mat rLx Variates
4.4 Correlation Priors
4.4.1 Intraclass
4.4.2 Markov
5 Hyperparameter Assessment
5.1 Introduction
5.2 Binomial Likelihood
5.2.1 Scalar Beta
5.3 Scalar Normal Likelihood
5.3.1 Scalar Normal
5.3.2 Inverted Gamma or Scalar Inverted Wishart
5.4 Multivariate Normal Likelihood
5.4.1 Multivariate Normal
5.4.2 Inverted Wishart
5.5 Matrix Normal Likelihood
5.5.1 Mat rL, c Normal
5.5.2 Inverted Wishart
6 Bayesian Estimation Methods
6.1 Marginal Posterior Mean
6.1.1 Mat rL, c Integration
6.1.2 Gibbs Sampling
6.1.3 Gibbs Sampling Convergence
6.1.4 Normal Variate Generation
6.1.5 Wishart and Inverted Wishart Variate Generation
6.1.6 Factorization
6.1.7 Rejection Sampling
6.2 Maximum a Posteriori
6.2.1 Mat rL, c Differentiation
6.2.2 Iterated Conditional Modes (ICM)
6.3 Advantages of ICM over Gibbs Sampling
6.4 Advantages of Gibbs Sampling over ICM
7 Regression
7.1 Introduction
7.2 Normal Samples
7.3 Simple Linear Regression
7.4 Multiple Linear Regression
7.5 Multivariate Linear Regression

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kxjs2007

2010-6-11 07:59:05

II Models
8 Bayesian Regression
8.1 Introduction
8.2 The Bayesian Regression Model
8.3 Likelihood
8.4 Conjugate Priors and Posterior
8.5 Conjugate Estimation and Inference
8.5.1 Marginalization
8.5.2 Maximum a Posteriori
8.6 Generalized Priors and Posterior
8.7 Generalized Estimation and Inference
8.7.1 Marginalization
8.7.2 Posterior Conditionals
8.7.3 Gibbs Sampling
8.7.4 Maximum a Posteriori
8.8 Interpretation
8.9 Discussion
9 Bayesian Factor Analysis
9.1 Introduction
9.2 The Bayesian Factor Analysis Model
9.3 Likelihood
9.4 Conjugate Priors and Posterior
9.5 Conjugate Estimation and Inference
9.5.1 Posterior Conditionals
9.5.2 Gibbs Sampling
9.5.3 Maximum a Posteriori
9.6 Generalized Priors and Posterior
9.7 Generalized Estimation and Inference
9.7.1 Posterior Conditionals
9.7.2 Gibbs Sampling
9.7.3 Maximum a Posteriori
9.8 Interpretation
9.9 Discussion
10 Bayesian Source Separation
10.1 Introduction
10.2 Source Separation Model
10.3 Source Separation Likelihood
10.4 Conjugate Priors and Posterior
10.5 Conjugate Estimation and Inference
10.5.1 Posterior Conditionals
10.5.2 Gibbs Sampling
10.5.3 Maximum a Posteriori
10.6 Generalized Priors and Posterior
10.7 Generalized Estimation and Inference
10.7.1 Posterior Conditionals
10.7.2 Gibbs Sampling
10.7.3 Maximum a Posteriori
10.8 Interpretation
10.9 Discussion
11 Unobservable and Observable Source Separation
11.1 Introduction
11.2 Model
11.3 Likelihood
11.4 Conjugate Priors and Posterior
11.5 Conjugate Estimation and Inference
11.5.1 Posterior Conditionals
11.5.2 Gibbs Sampling
11.5.3 Maximum a PosterJori
11.6 Generalized Priors and Posterior
11.7 Generalized Estimation and Inference
11.7.1 Posterior Conditionals
11.7.2 Gibbs Sampling
11.7.3 Maximum a PosterJori
11.8 Interpretation
11.9 Discussion
12 FMRI Case Study
12.1 Introduction
12.2 Model
12.3 Priors and Posterior
12.4 Estimation and Inference
12.5 Simulated FMRI Experiment
12.6 Real FMRI Experiment
12.7 FMRI Conclusion

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kxjs2007

2010-6-11 07:59:24

III Generalizations
13 Delayed Sources and Dynamic Coefficients
13.1 Introduction
13.2 Model
13.3 Delayed Constant Mixing
13.4 Delayed Nonconstant Mixing
13.5 Instantaneous Nonconstant Mixing
13.6 Likelihood
13.7 Conjugate Priors and Posterior
13.8 Conjugate Estimation and Inference
13.8.1 Posterior Conditionals
13.8.2 Gibbs Sampling
13.8.3 Maximum a Posteriori
13.9 Generalized Priors and Posterior
13.10 Generalized Estimation and Inference
13.10.1 Posterior Conditionals
13.10.2 Gibbs Sampling
13.10.3 Maximum a Posteriori
13.11 Interpretation
13.12 Discussion
14 Correlated Observation and Source Vectors
14.1 Introduction
14.2 Model
14.3 Likelihood
14.4 Conjugate Priors and Posterior
14.5 Conjugate Estimation and Inference
14.5.1 Posterior Conditionals
14.5.2 Gibbs Sampling
14.5.3 Maximum a Posteriori
14.6 Generalized Priors and Posterior
14.7 Generalized Estimation and Inference
14.7.1 Posterior Conditionals
14.7.2 Gibbs Sampling
14.7.3 Maximum a Posteriori
14.8 Interpretation
14.9 Discussion
15 Conclusion
Appendix A FMRI Activation Determination
A.1 Regression
A.2 Gibbs Sampling
A.3 ICM
Appendix B FMRI Hyperparameter Assessment
Bibliography

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yangxin789

2010-8-29 20:22:30

好书.但现在没钱,只好发给有钱的朋友帮下载.

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m8843620

2012-2-17 11:16:57

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