Introductory Books

Berry, D. A. (1996), Statistics: A Bayesian Perspective, London: Duxbury Press.

Bolstad, W. M. (2007), Introduction to Bayesian Statistics, 2nd ed. New York: John Wiley & Sons.

DeGroot, M. H. and Schervish, M. J. (2002), Probability and Statistics, Reading, MA: Addison Wesley.

Gamerman, D. and Lopes, H. F. (2006), Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, 2nd ed. London: Chapman & Hall/CRC.

Ghosh, J. K., Delampady, M., and Samanta, T. (2006), An Introduction to Bayesian Analysis, New York: Springer-Verlag.

Lee, P. M. (2004), Bayesian Statistics: An Introduction, 3rd ed. London: Arnold.

Sivia, D. S. (1996), Data Analysis: A Bayesian Tutorial, Oxford: Oxford University Press.

Intermediate-Level Books

Box, G. E. P., and Tiao, G. C. (1992), Bayesian Inference in Statistical Analysis, New York: John Wiley & Sons.

Chen, M. H., Shao Q. M., and Ibrahim, J. G. (2000), Monte Carlo Methods in Bayesian Computation, New York: Springer-Verlag.

Gelman, A. and Hill, J. (2006), Data Analysis Using Regression and Multilevel/Hierarchical Models, Cambridge: Cambridge University Press.

Goldstein, M. and Woof, D. A. (2007), Bayes Linear Statistics: Theory and Methods, New York: John Wiley & Sons.

Harney, H. L. (2003), Bayesian Inference: Parameter Estimation and Decisions, New York: Springer-Verlag.

Leonard, T. and Hsu, J. S. (1999), Bayesian Methods: An Analysis for Statisticians and Interdisciplinary Researchers, Cambridge: Cambridge University Press.

Liu, J. S. (2001), Monte Carlo Strategies in Scientific Computing, New York: Springer-Verlag.

Marin, J. M. and Robert, C. P. (2007), Bayesian Core: a Practical Approach to Computational Bayesian Statistics, New York: Springer-Verlag.

Press, S. J. (2002), Subjective and Objective Bayesian Statistics: Principles, Models, and Applications, 2nd ed. New York: Wiley-Interscience.

Robert, C. P. (2001), The Bayesian Choice, 2nd ed. New York: Springer-Verlag.

Robert, C. P. and Casella, G. (2004), Monte Carlo Statistical Methods, 2nd ed. New York: Springer-Verlag.

Tanner, M. A. (1993), Tools for Statistical Inference: Methods for the Exploration of Posterior Distributions and Likelihood Functions, New York: Springer-Verlag.

Advanced Titles

Berger, J. O. (1985), Statistical Decision Theory and Bayesian Analysis, New York: Springer-Verlag.

Bernardo, J. M. and Smith, A. F. M. (2007), Bayesian Theory, 2nd ed. New York: John Wiley & Sons.

de Finetti, B. (1992), Theory of Probability, New York: John Wiley & Sons.

Jeffreys, H. (1998), Theory of Probability, Oxford: Oxford University Press.

O’Hagan, A. (1994), Bayesian Inference, volume 2B of Kendall’s Advanced Theory of Statistics, London: Arnold.

Savage, L. J. (1954), The Foundations of Statistics, New York: John Wiley & Sons.

Books Motivated by Statistical Applications and Data Analysis

Carlin, B. and Louris, T. A. (2000), Bayes and Empirical Bayes Methods for Data Analysis, 2nd ed. London: Chapman & Hall.

Congdon, P. (2006), Bayesian Statistical Modeling, 2nd ed. New York: John Wiley & Sons.

Congdon, P. (2003), Applied Bayesian Modeling, New York: John Wiley & Sons.

Congdon, P. (2005), Bayesian Models for Categorical Data, New York: John Wiley & Sons.

Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. (2004), Bayesian Data Analysis, 3rd ed. London: Chapman & Hall.

Gilks, W. R., Richardson, S., and Spiegelhalter, D. J. (1996), Markov Chain Monte Carlo in Practice, London: Chapman & Hall.