Statistics - Probability versus Likelihood

Probability and likelihood are two related but distinct concepts in statistics.

Probability is a mathematical concept that assigns a value between 0 and 1 to describe the likelihood of an event. It represents the long-run proportion of times an event would occur if the experiment was repeated an infinite number of times.

Likelihood, on the other hand, is a function that describes the degree to which a particular set of data is consistent with a particular statistical model. It represents the probability of observing a particular set of data given a set of parameters in a statistical model.

In other words, probability measures the chance of an event happening, while likelihood measures the fit of a model to a given data set. Probability is a fixed value, while likelihood is a function that depends on the parameters of the model.

In statistical inference, likelihood is often used to estimate the parameters of a statistical model that best fit the data. The parameters that maximize the likelihood function are considered the most likely parameters given the data.

So, while both probability and likelihood are related to the concept of likelihood or chance, probability is a fundamental concept in probability theory, while likelihood is a concept specific to statistical models and their applications.