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Bayes Theorem
| Description: |
Bayes Theorem provides a method for calculating P(h | D), denoting the probability of h being correct, given a specific data set D.
Let
- P be a probability distribution,
- h be a hypothesis and
- D be a data set.
If we know
- P(h), the probability of hypothesis h being correct,
- P(D), the probability of data set D being observed, and
- P(D | h), the probability of observing D, under the assumption
of h being correct,
then Bayes Theorem provides a method for calculating P(h | D),
denoting the probability of h being correct, given a specific data
set D.
Bayes Theorem:
P(h | D) = P(D | h) * P(h) / P(D)
An application of Bayes Theorem:
- Given a data set D, find a hypothesis h ∈ H with highest
posteriori probability P(h | D).
- Method: Chose a hypothesis h ∈ H that maximizes the
expression P(D | h) * P(h).
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