Probability vs. Likelihood: What’s the difference?

TL’DR

• Use probability if you want to measure the fitness of data given a specific distribution
• Use likelihood if you want to measure the fitness of a model given some data

Probability

Probability is used to estimate how probable a sample or groups of samples are from a distribution based on a given distribution.

Probability refers to the area under curve (AUC) on the distribution curve. The higher the value, the more probable that the data come from this distribution.

Probability = P(data| distribution)  # measures how probable data come from the specific distribution

Likelihood

Likelihood is used to estimate how good a model fits the data

Likelihood refers to a specific point on the distribution curve. The lower the likelihood, the worse the model fits the data.

Likelihood = L(distribution| data) # measures how probable a specific distribution fits the given data

Example