Conclusion ¶
Bayes theorem is a powerful and complex tool for reasoning about the world around us. In this manual, a very narrow, but generally useful, approach has been presented. Then the singular solution process was applied repeatedly to many example problems. The risk here is leaving someone with the impression that this is the one and only way to solve a problem with Bayes theorem. In truth, this manual focused on a very narrow area of Bayesian statistics. Curious readers might want to skim the theory section to get a flavor for some of the other applications of Bayes theorem, or investigate some of the additional references .
Hopefully there are a couple of major points that a reader can take away when reading this manual:
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Bayes theorem can easily be applied to practical every day problems.
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The intuition from Bayes theorem is more important than running the actual numbers.
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Subjective probabilities are opinions, so you need to be aware of your own limitations when setting your priors and likelihoods.
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The use of Bayes theorem forces you to explicitly define your beliefs, which can lead to a productive discussion with others about why you made certain choices in your reasoning.