Bayes' Rule

The intuition behind Bayesian classification is use Bayes' rule to transform 5.1 into a product of two probabilities, each of which is easier to compute than

Substituting into

we obtain

w= argmax

• We can estimate P(w) from the frequency of the word.
• As we shall see, is also easy to estimate.
• P(O), the probability of the observation sequence, is harder to estimate, but we can ignore it.