Jethro's Braindump

Jeffreys Prior

The Jeffrey’s prior is an easy-to-compute reference prior that is invariant to transformation, used in Bayesian Inference. If the model only has a univariate parameter \(\theta\), the prior is given by:

\begin{equation} p(\theta) \propto \sqrt{I(\theta)} \end{equation}

where \(I(\theta)\) is the expected Fisher information in the model.

If \(\mathbf{\theta}\) is multi-dimensional, then the Jeffrey’s prior is given by:

\begin{equation} p(\theta) \propto \sqrt{\operatorname{det}\{l(\theta)\}} \end{equation}

where I is the Fisher information matrix. When the number of dimensions is large, this method becomes cumbersome. A common approach is to obtain non-informative priors for the parameters individually, and form the joint prior as a product of these individual priors.