**Motivation** We often don't have a [[probability distribution]] but we do have data (measurements, observations). **Idea** The likelihood is a measure of how well the data matches a probability distribution. i.e. if we were to pick an arbitrary set of parameters for a probability distribution, we can measure the likelihood of those parameters explaining the observed data $L(\mu = 14, \sigma = 0.4 | d)$ **Idea** Likelihood isn't a probability measure but will be proportional to a probability. $ L(\theta) \propto P(x | \theta) $ ## References - [Likelihood Estimation - THE MATH YOU SHOULD KNOW!](https://www.youtube.com/@CodeEmporium) --- - Links: [[Statistics]]