This book focuses on Bayesian multivariate inference, which is defined as any inference that involves a multivariate (marginal) posterior distribution and is distinct from frequentist multivariate inference in that that is defined as any analysis with a multivariate response variable. This text features multivariate models, including the mutivariate normal and t distributions, Dirichlet-multinomial and gamma-poisson models, and generalized mixed linear models. Experimental design techniques are also covered and include blocking and repeated measures; experimental planning principles (Bayesian stopping and decision rules in experiments to prove); and risk assessments such as a-priori Type I and Type II error risks in such experiments. Decision analysis is presented in this context as a coherent way to compute stopping boundaries and terminal decisions. Planning principles for experiments include information maximization. Each chapter includes problem sets and computer exercises.