to CASt bibliographies
by Andrew Gelman, John Carlin, Hal Stern
& Donald Rubin
(2nd ed, 2003). Well-respected and popular graduate textbook on
Bayesian inference and modelling. Includes single- and
multi-parameter models, large-sample inference, hierarchical models,
sensitivity analysis, experiment design, regression models, mixture
models, missing data, and computational issues (EM algorithm, posterior
simulation, Metropolis algorithm, Gibbs sampler).
Logical Data Analysis for the Physical Sciences
by P. C. Gregory (2005). The first monograph by an astronomer on Bayesian statistical methods. Covers the elements of Bayesian inference, maximum entropy probabilities, Markov chain Monte Carlo, and Bayesian approaches to spectral analysis (e.g. periodic time series) and Poisson sampling.
Data Analysis: A Bayesian Tutorial
by Devinderjit S. Sivia & John Skilling (2nd ed, 2006). Introduction
Bayesian methodology for scientists and engineers. Includes parameter estimation, model selection, nonparametric estimation, experimental design, least-squares extensions, error propagation, nested sampling, and image processing.
Decision Theory and Bayesian Analysis
by James O. Berger (2nd ed,
1985). Authoritative and
popular graduate-level textbook on Bayesian methodology. Covers
concepts (loss function, prior information, Bayesian inference),
empirical Bayes, hierarchical Bayes, robustness, computation, minimax
methods, invariance, sequential analysis, complete classes.
Chain Monte Carlo in Practice
by W. R.
Gilks, S. Richardson & D. J. Spiegelhalter
(1996). A multi-author discussion of MCMC computational issues in
Bayesian modeling, with applications in many fields (including
astronomy). Topics include Markov chain concepts, state-space
modeling, computational strategies & convergence, hypothesis
testing and model selection, model improvement, variable selection, EM
algorithm, hierarchical & nonlinear models, image analysis,
measurement error, mixture models.
and Empirical Bayes Metehods for Data Analysis
Bradley P. Carlin & Thomas A. Louis (2nd ed,
2000). Graduate-level volume on Bayesian computation with examples from
biomedicine and WinBUGS software. Topics include an introduction
to Bayesian inference, empirical Bayes approach, comparison with
frequentist procedures, MCMC computation, model criticism &
selection, decision theory, and special cases.