# Naive Bayes Algorithm

Abstract:
The Naive Bayes algorithm is a prediction and classification algorithm. It uses Bayes’ Theorem, a formula that calculates a probability by counting the frequency of values and combinations of values in the historical data. Naïve bayes algorithm is used in data mining process. Data mining is a process of analyzing patterns from historical information and transform it into an understandable structure for future use. Typical use of data mining process is in Science fields where analysts indentifies the patterns based on historical data available and use those patterns to predict future activities. It is also used in medical fields, like whether a patient has heart disease or not from his historical data like patient’s age, blood sugar level and other symptoms.
Description:
Naïve bayes algorithm is based on three concepts,
Prior : Past experience
Likelihood: chance of event could happen.
Posterior: predicting the event will occur

Prob(B given A) = Prior * Prob(A and B)/Prob(A)
Example: Support you would like to determine the possibility that people over 60 ages are more prone to heart disease. In this case, prior condition (A) would be over 60 and dependent condition (B) would be having heart disease.
If there are 100 persons randomly tested for heart disease and before testing it is already known that out of them 25 are having heart disease,
Probability of A and B, (means people are tested and have heart disease previously) = 25%
If 75 of the 100 patients are over 60, then
Probability of (A)= 75%
Then in this case, Bayes Theorem would predict that that 33% of the patients over 60 are likely prone to heart disease (25/75).