Bayesian Exam || All Answers Are Correct 100%.

Probability in Bayesian terms (as opposed to classical) correct answers How confident you are that a hypothesis is true Time in Bayesian vs. Classical correct answers Generally you cannot update classical models as time goes on, you can with Bayesian Product Rule correct answers P(A, B) = P(A) * P(B|A) *** Only if A and B are independent Sum Rule correct answers P(A) = P(B) * P(A|B) + P(nB)*P(A|nB) (nB is not B) OR P(A) = Σ P(Bi) * P(A|Bi) Bayes' Rule correct answers P(H|D) = P(H) * P(D|H) ------------------ P(D) Pieces of Bayes' Rule (posterior depends on) correct answers 1. Prior Probability 2. Likelihood 3. The P(D) in the denominator Prior effect on Post correct answers If hypothesis was plausible before data, then that helps it to be plausible after Likelihood effect on Post correct answers If the hypothesis assigned a high probability to the data (i.e. it predicted the data) then it is rewarded Marginal Likelihood: P(D) correct answers If the data would have happened anyway even if H were false, then a high likelihood doesn't mean much Sequential use of Bayes' correct answers Today's posterior is tomorrow's prior Bayes' rule with multiple hypotheses about a parameter, given data x=3 correct answers P(θ=1|x=3) = P(θ=1)P(x=3|θ=1) ------------------------ P(x=3) P(θ=2|x=3) = P(θ=2)P(x=3|θ=2) ------------------------