Multivariate Bayesian Statistics
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Applied Multivariate Analysis
Author: S. James Press
language: en
Publisher: Courier Corporation
Release Date: 2012-09-05
Geared toward upper-level undergraduates and graduate students, this two-part treatment deals with the foundations of multivariate analysis as well as related models and applications. Starting with a look at practical elements of matrix theory, the text proceeds to discussions of continuous multivariate distributions, the normal distribution, and Bayesian inference; multivariate large sample distributions and approximations; the Wishart and other continuous multivariate distributions; and basic multivariate statistics in the normal distribution. The second half of the text moves from defining the basics to explaining models. Topics include regression and the analysis of variance; principal components; factor analysis and latent structure analysis; canonical correlations; stable portfolio analysis; classifications and discrimination models; control in the multivariate linear model; and structuring multivariate populations, with particular focus on multidimensional scaling and clustering. In addition to its value to professional statisticians, this volume may also prove helpful to teachers and researchers in those areas of behavioral and social sciences where multivariate statistics is heavily applied. This new edition features an appendix of answers to the exercises.
Bayesian Data Analysis, Third Edition
Now in its third edition, this classic book is widely considered the leading text on Bayesian methods, lauded for its accessible, practical approach to analyzing data and solving research problems. Bayesian Data Analysis, Third Edition continues to take an applied approach to analysis using up-to-date Bayesian methods. The authors—all leaders in the statistics community—introduce basic concepts from a data-analytic perspective before presenting advanced methods. Throughout the text, numerous worked examples drawn from real applications and research emphasize the use of Bayesian inference in practice. New to the Third Edition Four new chapters on nonparametric modeling Coverage of weakly informative priors and boundary-avoiding priors Updated discussion of cross-validation and predictive information criteria Improved convergence monitoring and effective sample size calculations for iterative simulation Presentations of Hamiltonian Monte Carlo, variational Bayes, and expectation propagation New and revised software code The book can be used in three different ways. For undergraduate students, it introduces Bayesian inference starting from first principles. For graduate students, the text presents effective current approaches to Bayesian modeling and computation in statistics and related fields. For researchers, it provides an assortment of Bayesian methods in applied statistics. Additional materials, including data sets used in the examples, solutions to selected exercises, and software instructions, are available on the book’s web page.
Multivariate Bayesian Statistics
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