This is a graduate-level textbook on Bayesian analysis blending
modern Bayesian theory, methods, and applications. Starting from
basic statistics, undergraduate calculus and linear algebra, ideas
of both subjective and objective Bayesian analysis are developed to
a level where real-life data can be analyzed using the current
techniques of statistical computing.
Advances in both low-dimensional and high-dimensional problems
are covered, as well as important topics such as empirical Bayes
and hierarchical Bayes methods and Markov chain Monte Carlo (MCMC)
techniques.
Many topics are at the cutting edge of statistical research.
Solutions to common inference problems appear throughout the text
along with discussion of what prior to choose. There is a
discussion of elicitation of a subjective prior as well as the
motivation, applicability, and limitations of objective priors. By
way of important applications the book presents microarrays,
nonparametric regression via wavelets as well as DMA mixtures of
normals, and spatial analysis with illustrations using simulated
and real data. Theoretical topics at the cutting edge include
high-dimensional model selection and Intrinsic Bayes Factors, which
the authors have successfully applied to geological mapping.
The style is informal but clear. Asymptotics is used to
supplement simulation or understand some aspects of the
posterior.
General
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