 \(P(d\given H_x)\) and \(P(H_x)\) can be estimated from the given training dataset. Then the hypothesis with the highest posterior probability is then given as the answer and is given by: \(\argmax_{x}P\left(d\ggiven H_x\right)*P\left(H_x\right) \) In addition to probabilistic methods being used to build algorithms, probability theory has also been used to analyze algorithms which might not have an overt probabilistic or logical formulation. For example, one of the central classes of meta-theorems in learning, probably approximately correct (PAC) theorems, are cast in terms of lower bounds of the probability that the mismatch between the induced/learnt fL function and the true function fT being less than a certain amount, given that the learnt function fL works well for a certain number of cases (see Chapter 18, AIMA). 