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

----- 多元贝叶斯统计

ISBN: 9780367454661 出版年：2002 页码：350 Rowe, Daniel B Chapman and Hall/CRC

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