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
Index