Thompson Sampling
Thompson sampling draws a plausible success rate for each arm from its posterior and plays the largest draw. Uncertain arms get tried in proportion to how likely they are to be best.
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Posterior belief
Posterior beliefs depend on stated assumptions. Coherence, interval coverage, prior sensitivity, and new evidence test different aspects of the claim.
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Prior Belief (or Prior Probability)
A prior specifies assumptions before the analyzed data. Its concentration, parameterization, predictive implications, and sensitivity all affect the posterior.
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Bayes’ Theorem
Bayes’ theorem combines prior probabilities and likelihoods. A counting example shows why reversing conditional probabilities gives the wrong answer.
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Bayesian Inference
Expected loss from shipping 0.137729, from holding 0.094212. The point estimate of 0.70 says ship.