Hyperparameter

In Bayesian statistics, a hyperparameter is a parameter of a prior distribution; the term is used to distinguish them from parameters of the model for the underlying system under analysis.

This article is about hyperparameters in Bayesian statistics. It is not to be confused with Hyperparameter (machine learning).
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Bayesian statistics
Posterior = Likelihood × Prior ÷ Evidence
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For example, if one is using a beta distribution to model the distribution of the parameter p of a Bernoulli distribution, then:

  • p is a parameter of the underlying system (Bernoulli distribution), and
  • α and β are parameters of the prior distribution (beta distribution), hence hyperparameters.

One may take a single value for a given hyperparameter, or one can iterate and take a probability distribution on the hyperparameter itself, called a hyperprior.

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