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I am looking for a textbook that is a nice entry level to Bayesian Inference. I was hoping that there is a nice blend of theory and applications (data sets) on how concepts are applied. Programming techniques presented are welcome.

Just for perspective, I feel that Christopher Bishop's PRML is a theoretical treatment. It is very good theoretically, but I find myself not understanding how to apply it given a data set.

I have tried jumping from one book to another and this has just confused me. Is there any authoritative book with these requirements?

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  • $\begingroup$ Are you asking about inference in Bayesian graph? $\endgroup$
    – hanugm
    Commented Aug 11, 2021 at 12:30
  • $\begingroup$ Sorry, not about Bayesian graphs, but Bayesian inference in general. $\endgroup$
    – cgo
    Commented Aug 12, 2021 at 9:56

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Using as a best reference accordingly my own google research, find the best post about best introductory Bayesian statistics book and summarize the answers. I find this post in stats.stackexchange about bayesian statistics books maybe this is the best recomendation for you. I read the post weeks ago and some books are stunning.

This is my TOP 3 books from the answer from stats this books repeat themselves in answers below (all the books have applications)

  1. Doing Bayesian Data Analysis: A Tutorial with R and BUGS.
  2. Bayesian Data Analysis 3rd Andrew Gelman
  3. Statistical Rethinking A Bayesian Course with Examples in R and Stan Second Edition Richard McElreath

I start reading Bayesian Data Analysis 3rd Andrew Gelman days ago I am in the first chapter about Bayesian Inference you can check the first chapter:

Part I: Fundamentals of Bayesian Inference 1
1 Probability and inference 3 
1.1 The three steps of Bayesian data analysis 3
1.2 General notation for statistical inference 4 
1.3 Bayesian inference 6
1.4 Discrete probability examples: genetics and spell checking 8
1.5 Probability as a measure of uncertainty 11
1.6 Example of probability assignment: football point spreads 13
1.7 Example: estimating the accuracy of record linkage 16
1.8 Some useful results from probability theory 19
1.9 Computation and software 22
1.10 Bayesian inference in applied statistics
24 1.11 Bibliographic note 25
1.12 Exercises 27

and also the book have the Chapter 10 Introduction to Bayesian computation..

Some people prefer some book than others for understand Bayesian Statistics so you have to choose which one fits you, for example statistical rethinking is a different than other books is another way to explain bayesian statistics some people not understand. but is the best 3 from the post.

Just take a look the chapter difference between Gelman and Statistical Rethinking

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