logo

Video encyclopedia

Likelihood function

2:12

What is Likelihood? (And why do we care?)

2:11

What is log likelihood and why do we use it?

2:43

5. MLE Example: Uniform

1:56

Maximum Likelihood Estimation (MLE): The Intuition

0:52

Likelihood 1 - Intro to Statistics

In frequentist inference, a likelihood function is a function of the parameters of a statistical model, given specific observed data. Likelihood functions play a key role in frequentist inference, especially methods of estimating a parameter from a set of statistics. In informal contexts, "likelihood" is often used as a synonym for "probability". In mathematical statistics, the two terms have different meanings. Probability in this mathematical context describes the plausibility of a random outcome, given a model parameter value, without reference to any observed data. Likelihood describes the plausibility of a model parameter value, given specific observed data.
  • Definition 

  • Likelihood ratio and relative likelihood 

  • Likelihoods that eliminate nuisance parameters 

  • Products of likelihoods 

  • Log-likelihood 

  • Background and interpretation