Data analysis recipes: Probability calculus for inference

Understand

In this pedagogical text aimed at those wanting to start thinking about or brush up on probabilistic inference, I review the rules by which probability distribution functions can (and cannot) be combined.

• I connect these rules to the operations performed in probabilistic data analysis.
• Dimensional analysis is emphasized as a valuable tool for helping to construct non-wrong probabilistic statements.
• The applications of probability calculus in constructing likelihoods, marginalized likelihoods, posterior probabilities, and posterior predictions are all discussed.