Terms in Bayes Theorem

Descriptions of different terms of the bayes theorem.

What is bayes theorem?

Bayes theorem determines a probability of an occurrence of an event based on the prior knowledge of occurrence of that event or knowledge of conditions that may lead to the occurrence of the event.

The bayes theorem is represented by the below equation:

# Bayes Theorem
P( y=1 | x = x⁰) = P( x=x⁰ | y=1) P(y=1)
                   ---------------------
                           P(x=x⁰)

Here is an image of the same in a simpler representation.

Source: wikipedia

Most of the times researchers and research papers involving application of bayes rule refer the terms in jargonic ways which are at times not easy to understand if you are not from the mathematical background.

Here lets try to see what terms are called by whats names.

Posterior or Posterior Probability

The term on the left of the ‘=’ sign in the equation is the posterior, i.e. the probability after we have calculated the known quantities.

# The Posterior
P( y=1 | x = x⁰)
       or
P( A | B )

Class Conditioned Probability or Likelihood

The known quantity of likelihood of occurrence of a class x⁰ given y is 1 is Likelihood or Class Conditioned Probability.

# Class Conditioned Probability or Likelihood
P( x=x⁰ | y=1)
       or
P( B | A )

A Priori or Prior Probability

The observed probability of the class is called A Priori or Prior Probability. In our case here it is P( y=1) or P(A)

# A Priori or Prior Probability
P(y=1)
  or
P(A)

Marginal or Evidence

The term in the denominator is termed as marginal or evidence.

# Marginal or Evidence
P(x=x⁰)
  or
P(B)

While reading papers I often struggle to remember these terms by the names. So I thought it would be nice to write a short post that I can refer to once I come across these terms.

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