The maximum likelihood prior
The maximum likelihood prior
Consider an estimate $\theta^*$ of a parameter $\theta$ based on repeated observations from a family of densities $f_\theta$ evaluated by the Kullback–Leibler loss function $K(\theta, \theta^*) = \int \log(f_\theta/f_{\theta^*})f_\theta$. The maximum likelihood prior density, if it exists, is the density for which the corresponding Bayes estimate is asymptotically negligibly different …