Tutorial: Prior knowledge, proportions and probabilities of probabilities

Alejandro Diaz, Institute for Risk and Uncertainty, University of Liverpool, UK SummaryWhich proportion is higher: 5 out of a 10, or 400 out of 1000? The answer seems obvious. But if these proportions were number of successes divided by number of trials, would you still think the same? Is a baseball player who achieved 5 hits out of 10 chances throughout his career, better than one who achieved 400 hits out of 1000 chances? In this introductory tutorial, we will see how Bayesian inference helps us add context in order to make decisions. The key will reside on representing prior knowledge using a probability distribution for probabilities: the very famous and elegant beta distribution.

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