# Jeffreys Prior / Jeffreys Rule Prior: Simple Definition

Jeffrey’s prior (also called Jeffreys-Rule Prior), named after English mathematician Sir Harold Jeffreys, is used in Bayesian parameter estimation. It is an uninformative prior, which means that it gives you vague information about probabilities. It’s usually used when you don’t have a suitable prior distribution available. However, you could choose to use an uninformative prior if you don’t want it to affect your results too much.

The uninformative prior isn’t really “uninformative,” because any probability distribution will have some information. However, it will have little impact on the posterior distribution because it makes minimal assumptions about the model.

## Jeffrey’s Prior Definition

Jeffreys prior is defined in terms of Fisher information, which tells us how much information about an unknown parameter we can get from a sample. In other words, Fisher Information tells us how well we can measure a parameter, given a certain amount of data. The formula for Jeffreys prior is:

Where:

Jeffreys prior is especially useful because it is invariant under reparameterization of the given parameter vector.

## Is it “Prior” or “Rule-Prior”?

Jeffreys didn’t always stick to using the Jeffreys rule prior he derived. For example, for the Poisson mean λ, he recommended
p(λ) α 1/λ,