## What is the difference between Prior Probability and Posterior Probability?

**Prior Probability**

A prior probability is the probability that an observation will fall into a group before you collect the data. The prior is a probability distribution that represents your uncertainty over θ **before **you have sampled any data and attempted to estimate it – usually denoted π(θ).

**Posterior Probability**

A posterior probability is the probability of assigning observations to groups given the data. The posterior is a probability distribution representing your uncertainty over θ **after** you have sampled data – denoted π(θ|X). It is a conditional distribution because it conditions on the observed data.

From Bayes’ theorem we relate the two:

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