STAT 4444 Study Guide - Midterm Guide: Posterior Probability, Sequential Analysis, Fair Coin
6 Mar 2020
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P (m odel|data) p (m odel) p (data|m odel) (1) In a bayesian setting, the newly collected data makes the probability distribution over the parameter narrower. The posterior distribution over the possible parameter values allows bayesians to take into account the uncertainty in the estimate by integrating the full posterior distribution instead of basing the prediction just on the most likely value. A bayesian sequential analysis can be performed to ne-tune the model and improve its accuracy. If a b = , then sets a, b are mutually exclusive or disjoint. The probability that at least one of the two events a, b occurs is: P (a b) = p (a) + p (b) p (a b) If events a, b are mutually exclusive, then: example: consider events a, b, c, d. P (a b) = p (a) + p (b)
