Bayesian Option Value

Given a distribution for F and option values, how do we compute the posterior distribution.

Example

P(AB) = P(A)P(B|A) = P(B)P(A|B)

P(A|B) = P(A)P(B|A)/P(B).

P(X = x) = q^x(1-q)^{1-x}, x\in\{0,1\}, 0\le q\le 1.

P(X = x|X_1 = x_1) = P(X = x)P(X_1 = x_1|X = x)/P(X = x)