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Interested in self-study?
Having a textbook that includes over 100 worked examples is, in my opinion, ideal for self-study. This also provides an opportunity for students to tailor the time commitment devoted to your inquiry into Bayesian data analysis.
Obviously, my first and best recommendation is to work through the book in its entirety. This will give you the most complete view of the basics of Bayesian data analysis as well as how the techniques I describe are derived directly from the two rules of probability theory.
Nevertheless, I understand that this is a substantial project, and there are some who would like to jump-start their understanding of Bayesian data analysis without completing every page of the book. This may particularly be the case if you have a background in science or in classical statistical hypothesis testing, and may therefore not need some of the material included in a fully self-contained course book. For those, I offer the following recommendations:
In aiming for a complete understanding of the basics and their place within Bayesian data analysis I included two concepts that round out the topic of Bayesian analysis, but are not strictly necessary if you want to jump right in and get started analyzing basic data. These are prediction and decision, and are contained in Chapter 5.
If you come to the table with a background in science or classical frequentist statistics, you should already be familiar with basic summary statistics and data visualization techniques described in the later portions of Chapter 1. Further, if you are familiar with basic sampling distributions (Gaussian, binomial, Poisson, etc.) you could also skip the initial portions of Chapter 3, focusing on the three types of prior distribution (pages xx - xx) and the fully worked Gaussian example of combining prior and likelihood to produce a posterior distribution (pages xx - xx). Finally, Chapter 2 contains a number of example problems that are intended to provide familiarity with making basic probability calculations. If you do not need this practice you could skip that material and focus on manipulating probability expressions (pages xx - xx), marginalization (xx -xx), and computing probability distributions (pages xx - xx).
Finally, if your focus is only on hypothesis testing (model selection), you may consider skipping the bulk of Chapter 5 which covers the topic of Measurement. I would not recommend skipping the entire chapter, however, because Measurement calculations are contained within Model Selection, and it is important to clearly differentiate these two very different data analytic techniques. If you want to skip my full treatment of the topic of measurement, I would still recommend reading pages xx - xx to get an understanding of these calculations (so that they won't be overwhelming when you have to incorporate them into your model selection computations).
Shortest Basic Self-Study
All together, if you already have a background in classical statistics and your goal is to learn the Bayesian method of testing scientific hypotheses, you could probably get away with the following:
along with completing the relevant worked examples.
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