Bayesian

Bayesian

1. Probability

   • Basics
     • Independent: P(AnB) = P(A) x P(B)
     • Conditional: P(AnB) = P(A|B) x P(B)
     • Marginalisation
       • P(A) = P(A|B) P(B) + P(A|B') P(B')
       • P(A) = P(AnB) + P(AnB')
     • Fundamental rule: P(A|B) = P(A,B)/P(B)
     • Bayes: P(A|B) = [P(B|A) x P(A)]/P(B)
       • Update posterior based on evidence using prior
       • Prior P(A)
       • Posterior P(A|B)
       • Likliehood P(B|A)
       • Marginalisation P(B)
     • Axioms
       • Multiplication rule
         • P(E1nE2) = P(E1) x P(E2) for independent
         • P(E1nE2) = P(E1) x P(E2|E1) for dependant
         • Chain rule: P(A,B,C) = P(B|A,C) x P(A|C) x P(C)
       • Addition rule
         • P(AuB) = P(A) + P(B) for mutually exclusive
         • P(AuB) = P(A) + P(B) - P(AnB)
       • Unit measure: 0 <= P <= 1
       • Unit sum: P(omega) = 1
     • Joint probability: P(A,B) A and B occuring same time
   • Distributions
     • Combinations: n!/r! x (n-r)!
       • Use ncr to avoid listing combinations
       • Binomial: comb(n,r) p^r x (1-p)^n-r
     • Permutations: n!/(n-r)!

2. Bayesian Networks

   • d-connections
     • Converging: B -> A <- C
     • Diverging: B <- A -> C
     • Serial: B -> A -> C
     • Follow arrows in consistent direction
     • Junction tree
       • 1) Join converging parents 2) Arrows to lines 3) Triangulation
   • Idioms
     • Cause-consequence: Cause -> Consequence
     • Measurement: Accuracy -> Assessed <- Actual
     • Definitional: S=D/T
     • Induction: Data <-> Observations