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I write here to ask for a suggestion about a graduate level Bayesian statistics book. I have a bachelor degree in statistics but despite having a fairly solid background on frequentist and non parametric statistics, I do not know much about Bayesian statistics.

In particular I am undecided between these two books:

  1. Doing Bayesian Data Analysis http://www.indiana.edu/~kruschke/DoingBayesianDataAnalysis/

  2. Statistical Rethinking https://www.crcpress.com/Statistical-Rethinking-A-Bayesian-Course-with-Examples-in-R-and-Stan/McElreath/p/book/9781482253443

Which one is right for me?

I know R very well, so the presence of examples on R is an added value.

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  • $\begingroup$ also consider Gelman and Hill Data Analysis Using Regression Analysis and Multilevel/Hierarchical Models and Gelman et al. Bayesian Data Analysis 3d ed. $\endgroup$
    – Ben Bolker
    Commented Aug 20, 2018 at 23:02
  • $\begingroup$ It might be helpful to find out a little bit more about you/why you're learning Bayesian stats: are you interested in applications? In any particular area? Big data? Data analysis? Theory? What are your other statistical interests (e.g. time series, spatial statistics, survival analysis, causal inference, ... ???) $\endgroup$
    – Ben Bolker
    Commented Aug 20, 2018 at 23:11
  • $\begingroup$ I have both those books - both are great and come with R code examples. I personally prefer Statistical Rethinking because of its style. Both books offer free sample chapters online, so I'd recommend you have a look yourself. $\endgroup$
    – Maurits M
    Commented Aug 21, 2018 at 7:19
  • $\begingroup$ @BenBolker Well I will study Bayesian statistics for a university course and I wanted a text that would explain the applications to be combined with the mathematics provided by the course. (The recommended books of the course are too theoretical for my taste). In particular, I'm interested in Big Data, Data analysis, time series and spatial statistics. $\endgroup$
    – Walter
    Commented Aug 21, 2018 at 8:37
  • $\begingroup$ @MauritsM Are the two books on the same level or one of the two is more advanced? $\endgroup$
    – Walter
    Commented Aug 21, 2018 at 8:40

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There are many useful graduate level books on Bayesian statstics, some of which focus more on theory and philosophy, and others focussing more on practical implementation. In my opinion, the best and most comprehensive guide to the underlying theory is Bernardo and Smith (2000). This book gives a solid philosophical and theoretical grounding that is unparalleled by any other book I have read. I consider it 'the Bible' of Bayesian statistics.

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