Understanding Bayes' theorem

There are quite a few scenarios where it would be really good to know how likely it is for our classifier to make a mistake. For example, in Chapter 5, Using Decision Trees to Make a Medical Diagnosis, we trained a decision tree to diagnose women with breast cancer based on some medical tests. You can imagine that, in this case, we would want to avoid a misdiagnosis at all costs; diagnosing a healthy woman with breast cancer (a false positive) would be both soul-crushing and lead to unnecessary, expensive medical procedures, whereas missing a woman's breast cancer (a false negative) might eventually cost the woman her life.

It's good to know we have Bayesian models to count on. Let's walk through a specific (and ...

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