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Which is the best introductory textbook for Bayesian statistics?

One book per answer, please.

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    $\begingroup$ In the replies, please explain why you are recommending a book as "the best." $\endgroup$ – whuber Jan 25 '12 at 15:33
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    $\begingroup$ How can there be more than one answer to a question question phrased like this? $\endgroup$ – naught101 Jul 24 '12 at 5:44
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    $\begingroup$ This is an old thread now, but I came back to +1 a new book "Statistical Rethinking. And in looking the higher-ranking answers in the thread, I think a key distinction hasn't been made: "introductory" for whom? A first course in statistics (that happens to have a Bayesian approach)? An introduction to Bayesian methods for someone with basic undergraduate (non-Bayesian) statistics classes? Or an introduction to Bayesian statistics for a practitioner of non-Bayesian statistics who has finally been persuaded that this Bayesian thing isn't a fad? Very different introductions. $\endgroup$ – Wayne Jan 20 '16 at 13:54

36 Answers 36

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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.

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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.

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I am now reading : From Algorithm to Z-Scores: Probabilistic and Statistical Modeling in Computer Science by Norm Matloff, UC Davis, freely available for download.

My two cents.

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We're looking for long answers that provide some explanation and context. Don't just give a one-line answer; explain why your answer is right, ideally with citations. Answers that don't include explanations may be removed.

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    $\begingroup$ Well, do you like it? Would you recommend it to others? Is it for math-savvy or math-phobic readers? $\endgroup$ – gung Sep 19 '14 at 12:05
  • $\begingroup$ I'm still reading Chapter 2, (Probability and Conditional Probability). A little math, nothing exoteric so far, and easy-to-read... I like the approach but is too early to draw a full opinion. I leeave you here the link to the book to download... let me know what you think: (heather.cs.ucdavis.edu/~matloff/132/PLN/ProbStatBook.pdf) $\endgroup$ – Fabio Sep 20 '14 at 17:36
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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.

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We're looking for long answers that provide some explanation and context. Don't just give a one-line answer; explain why your answer is right, ideally with citations. Answers that don't include explanations may be removed.

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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.

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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

Reference

Bayesian Methodology: An overview with the help of R software

ISBN-13: 978-1092939898

Link: https://books.google.ae/books?id=UnmQDwAAQBAJ&dq=Bayesian+Methodology:+An+overview+with+the+help+of+R+software&source=gbs_navlinks_s

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  • $\begingroup$ Please add a reference/link to that book! Authors? $\endgroup$ – kjetil b halvorsen Jul 11 at 8:35

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