Models for Source Separation and Signal Unmixing

scalar wishart

Rowe, D.B. (2003). Multivariate Bayesian Statistics: Models for Source Separation and Signal Unmixing. CRC Press, Boca Raton, FL, USA. ISBN: 1584883189. List price $79.95.

Annotation
Using a Bayesian approach, this book addresses the blind source separation problem important in diverse applications from areas such as acoustics, genetics, portfolio allocation, and signal processing. It provides all the background needed, then examines the instantaneous constant mixing model where both the observed vectors and unobserved sources are independent over time but can be dependent within each vector. The author presents two distinct ways of estimating parameter for each model and includes MATLAB code for each model discussed.



Table of Contents
Introduction

The Cocktail Party

The Source Separation Model
Part l: FUNDAMENTALS
STATISTICAL DISTRIBUTIONS
Scalar Distributions

Binomial

Beta

Normal

Gamma and Scalar Wishart

Inverted Gamma and Scalar Inverted Wishart

Student t

F Distribution
Vector Distributions

Multivariate Normal

Multivariate Student t
Matrix Distributions

Matrix Normal

Wishart

Inverted Wishart

Matrix T
INTRODUCTORY BAYESIAN STATISTICS
Discrete Scalar Variables
Continuous Scalar Variables
Continuous Vector Variables
Continuous Matrix Variables
PRIOR DISTRIBUTIONS
Vague Priors

Scalar Variates

Vector Variates

Matrix Variates
Conjugate Priors

Scalar Variates

Vector Variates

Matrix Variates
Generalized Priors

Scalar Variates

Vector Variates

Matrix Variates
Correlation Priors

Intraclass

Markov
HYPERPARAMETER ASSESSMENT
Introduction
Binomial Likelihood

Scalar Beta
Scalar Normal Likelihood

Scalar Normal

Inverted Gamma or Scalar Inverted Wishart
Multivariate Normal Likelihood

Multivariate Normal

Inverted Wishart
Matrix Normal Likelihood

Matrix Normal

Inverted Wishart
BAYESIAN ESTIMATION METHODS
Marginal Posterior Mean

Matrix Integration

Gibbs Sampling

Gibbs Sampling Convergence

Normal Variate Generation

Wishart and Inverted Wishart Variate Generation

Factorization

Rejection Sampling
Maximum a Posteriori

Matrix Differentiation

Iterated Conditional Modes (ICM)
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 (Multivariate)
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
Index

Link to Matlab programs and Data Sets

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