Learnings and experiments with statistical modeling

How to think about Bayes Theorem

1. A way to compute likelihood of a hypothesis, given some data (may be easier to compute this way)
2. A way of updating beliefs, when we see more data

H = Hypothesis D = Data or observation(s) made/seen P(H/D) = P(H) * P(D/H) / P(D)

Bayes Table (organizing calculations and scaling)

P(H) = Priors = Probability of Hypothesis (before data) P(D/H) = Likelihood of getting data, assuming hypothesis is true (hypothesis event happened) P(D) = Probability of data being observed regardless of whether hypothesis is true or not

Law of total probability (depending on how many hypothesis) Assuming H1, H2,... are mutually exclusive. Only one happens at a time P(D) = P(H1)*P(D/H1) + P(H2)*P(D/H2) + ....