Multivariate Bayesian Statistics: Models for Source Separation and Signal Unmixing (Hardcover)

IntroductionPart 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 REGRESSIONIntroductionThe Bayesian Regression ModelLikelihoodConjugate Priors and Posterior Conjugate Estimation and Inference Generalized Priors and Posterior Generalized Estimation and Inference Interpretation DiscussionBAYESIAN FACTOR ANALYSIS IntroductionThe Bayesian Factor Analysis ModelLikelihoodConjugate Priors and PosteriorConjugate Estimation and InferenceGeneralized Priors and PosteriorGeneralized Estimation and InferenceInterpretationDiscussionBAYESIAN SOURCE SEPARATIONIntroductionSource Separation ModelSource Separation LikelihoodConjugate Priors and PosteriorConjugate Estimation and InferenceGeneralized Priors and PosteriorGeneralized Estimation and InferenceInterpretationDiscussionUNOBSERVABLE AND OBSERVABLE SOURCE SEPARATIONIntroductionModelLikelihoodConjugate Priors and PosteriorConjugate Estimation and InferenceGeneralized Priors and PosteriorGeneralized Estimation and InferenceInterpretationDiscussionFMRI CASE STUDYIntroductionModelPriors and PosteriorEstimation and InferenceSimulated FMRI ExperimentReal FMRI ExperimentFMRI ConclusionPart III: Generalizations DELAYED SOURCES AND DYNAMIC COEFFICIENTSIntroductionModelDelayed Constant MixingDelayed Nonconstant MixingInstantaneous Nonconstant MixingLikelihoodConjugate Priors and PosteriorConjugate Estimation and InferenceGeneralized Priors and PosteriorGeneralized Estimation and InferenceInterpretationDiscussionCORRELATED OBSERVATION AND SOURCE VECTORSIntroductionModelLikelihoodConjugate Priors and PosteriorConjugate Estimation and InferencePosterior ConditionalsGeneralized Priors and PosteriorGeneralized Estimation and InferenceInterpretationDiscussionCONCLUSIONAppendix A FMRI Activation DeterminationAppendix B FMRI Hyperparameter AssessmentBibliographyIndex