Which is the best introductory textbook for Bayesian statistics?
One book per answer, please.
Bayesian Modeling Using WinBUGS by Ioannis Ntzoufras, 2009.
Not only does this book introduce Bayesian methods, but includes everything one needs to immediately start running and diagnosing Bayesian models from simple normal models to generalized linear models to Bayesian hierarchical models. Not impressed yet? An entire chapter on how to set up and run WinBUGS (also useful for OpenBUGS!). Pseudo code and R code side-by-side throughout the book. Everything is illustrated with hands on examples. Also included are a chapter on the predictive distribution and model checking, and a chapter on checking convergence.
It is such an excellent combination of theory, explanation, application, software instruction and code.
Computational Bayesian Statistics by Turkman et. al. is a high-quality and all-inclusive introduction to Bayesian statistics and its computational aspects. It has the right mix of theory, model assessment and selection, and a dedicated chapter on software for Bayesian statistics (with code examples). It should serve nicely as a practical textbook for a first course in Bayesian methods.
I'd recommend the following:
Gelman et al (2013). Bayesian Data Analysis. CRC Press LLC. 3rd ed.
Hoff, Peter D (2009). A First Course in Bayesian Statistical Methods. Springer Texts in Statistics.
Kruschke, Doing Bayesian Data Analysis: A Tutorial with R and Bugs, 2011. Academic Press / Elsevier.
Albert, Jim (2009). Bayesian Computation with R. 2nd ed. Springer.
Bishop (2006). Pattern Recognition and Machine Learning (PRML)
If you have ever heard about The Elements of Statistical Learning (ESL), PRML can be treated as a bayesian version of it. The book talks about the most important models in statistical/machine learning from linear regression, NN, SVM to graphical models, all in bayesian perspective. The introduction to EM algorithm, variational inference and MCMC are well written.
Bayesian methodology differs from traditional statistical methodology which involves frequentist approach. Bayesian methodology is now widely being used due to its simple, straightforward and interpretable characteristics of probability values and the efficiency of modern day computer systems
The book covers the following topics:
1.Introduction to Bayesian Methodology 2.Bayesian concepts - types of priors and Markov Chain and Monte Carlo method 2 3.Bayesian inference - Binomial test 4.Bayesian inference - Poisson test 5.Bayesian inference – Student’s t test 6.Bayesian inference – Correlation Test 7.Bayesian Regression 8.Bayesian Linear Regression 9.Bayesian Logistic Regression 10.Bayesian probit Regression 11.Bayesian Quantile Regression 12.Bayesian Survival Analysis 13.Bayesian methodology in Machine Learning 14.Bayesian – Machine learning - Classification Models (supervised learning) 15.Bayesian – Machine learning - Topic Modeling (unsupervised learning) 16.Bayesian network
Bayesian Methodology: An overview with the help of R software