Page 41 - Data Science Algorithms in a Week

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Naive Bayes

A naive Bayes classification algorithm assigns a class to an element of a set which is most
probable according to Bayes' theorem.
Let A and B be probabilistic events. P(A) the probability of A being true. P(A|B) the
conditional probability of A being true given B is true. Then, Bayes' theorem states the
following:

P(A|B)=(P(B|A) * P(A))/P(B)

P(A) is the prior probability of A being true without the knowledge of the probability of
P(B) and P(B|A). P(A|B) is the posterior probability of A being true, taking into
consideration additional knowledge about the probability of B being true.

In this chapter, you will learn the following:

How to apply Bayes' theorem in a basic way to compute the probability of a
medical test being correct in simple example Medical test
To grasp Bayes' theorem by proving its statement above and its extension
How to apply Bayes' theorem differently for independent and dependent
variables in examples Playing chess
How to apply Bayes' theorem for discrete random variables in examples Medical
test and Playing chess; and for continuous random variables in example Gender
classification using the probability distribution of the continuous random
variable
To implement in Python an algorithm calculating the posterior probabilities
using Bayes' theorem in section Implementation of naive Bayes classifier
By verifying your understanding through solving problems in the end of the
chapter to discern in what situations Bayes' theorem is an appropriate method of
analysis and when it is not