Chapter 1 Tools of the trade

1. Basic idea of probability :

1) Relative frequency of occurrence of an event. Eg. Na/(Na+Nb+Nc) = 1/5;

2) A statement of the plausibility of occurrence of an event. Eg. a 40% chance to rain tomorrow.

2. Bayes’ theorem

•      P(B|A) = [P(A|B)*P(B)]/P(A)

=> P(A|B)+P(A|!B) = [P(A)+P(A|B)-2P(AB)]/[1-P(B)]

•      P(H|D) =  [P(D|H)*P(H)]/P(D)

H: Hypothesis; D: Experiment/Observations

P(H): Prior probability;  P(D|H): likelihood function of H; P(H|D): Posterior probability

P(H|D1D2) =  [P(D2|D1H)*P(D1|H)*P(H)]/P(D2D1)

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