The fundamental result that expresses a conditional probability P(A|B) of an event A given an event B as
More generally, where is one of a set of I events which together make up all possible eventualities (such as all of the 20 diseases under consideration),
This allows estimates of probability to be continually revised in the
light of new observations.
(Named after the English probabilist and theologian Thomas Bayes (1702-61)).
e.g. We may have an estimate of our belief in whether a cow is infected
with ECF given that
we have observed that it has enlarged lymph nodes: P(ECF | Lymph nodes
enlarged). If we
now observe that the animal is anaemic, this will change our belief
in whether it has the
disease. Our new belief can be calculated using Bayes' theorem.