I did an introductory course to Bayesian in my master's degree in Statistics. I did not understand much since it was too much in short time, very concentrated. We have covered from the most basic (bayes theorem), conjugate priors, but then moved fast to Method of composition, bayes regression, Gibbs sampler and Metropolis algorithm. I did not understand these last topics. Moreover, the software used was WinBUGS, that looked absolutely outdated and full of bugs. I would ask you, if there is any nice not outdated book about bayesian stats to read this summer. Also, I want to ask, what are the mainstream software in bayesian stats? All of them look deprecated.
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$\begingroup$ Of course, this is mainly opinion based, thus off-topic. But my impression is that WinBugs is used less often now than it was a few years ago. // Maybe if you say why you are interested in re-visiting Bayesian inference now and for what applications, you might get more useful answers. $\endgroup$– BruceETCommented Jun 16, 2022 at 20:22
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$\begingroup$ mc-stan.org $\endgroup$– dipetkovCommented Jun 16, 2022 at 20:24
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2$\begingroup$ Another popular option is Rethinking Statistics by McElreath, which has a set of accompanying Youtube videos. $\endgroup$– Jeremy MilesCommented Jun 16, 2022 at 21:27
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1$\begingroup$ Robert's books are excellent, focusing on concepts, instead of tools, and written with great care and good taste: amzn.to/3xWED9T $\endgroup$– ZenCommented Jun 16, 2022 at 21:43
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1$\begingroup$ @Zen: thanks for your kind words!!! $\endgroup$– Xi'anCommented Jun 17, 2022 at 6:33
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