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The conditional probability is an essential quantity in wide range of
domains, including classification, decision theory, prediction,
diagnostics, and other similar situations. That is because one typically makes the
classification, decision, prediction, etc. based on some
evidence. Thus, what one wants to know is the probability of
the result * given* the evidence . In the example of
classification, the evidence is the values of the measurements, or the
features on which the classification is to be based. The possible
results are the possible classes. The
problem is that this conditional probability is very difficult to
estimate from experiments directly. This is because there are
typically a huge number of values which the features can take. Thus
there would be an enormous number of conditional probabilities to
estimate. To get around this,
Bayes rule is used to write
this in terms of the conditional probability of getting the evidence
given the classification.
The probability of the evidence conditioned on the
result can sometimes be determined from first principles, and is
often
much easier to estimate. There are often only a handful of possible
classes or results. For a given
classification, one tries to measure the probability of getting
different evidence or patterns. A model is used to interpolate to
unseen patterns. This gives an estimate of the conditional probability
of the evidence given the classification. Using Bayes rule, we use
this to get what is desired, the conditional probability of the
classification given the evidence.

** Next:** Rules of Probability Calculation
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*Jon Shapiro*

*1999-09-23*