electrode

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The Wikipedia article has some decent examples of applying Bayes' theorem (and why it can yield some unintuitive results in the medical field).

Realistically though, I think this book assumes knowledge of the fundamentals of Bayesian stats already (which is a huge area). I'd recommend going through the early chapters of a Bayesian text (like Bayesian Data Analysis by Gelman et. al) to get a better feel for this.

I like the intuition behind Figure 1.15, and found it helpful to go through the proof of Eq 1.58 since it helps to put into context the $\frac{1}{N-1}$ used in calculating the unbiased variance estimate from a sample.