Empirical Bayes methods for learning prior distributions from data.
An unknown prior distribution (g) has yielded (unobservable) parameters, each of
which produces a data point from a parametric exponential family (f). The goal
is to estimate the unknown prior ("g-modeling") by deconvolution and Empirical
Bayes methods. Details and examples are in the paper by Narasimhan and Efron
(2020,

An unknown prior density $g(\theta)$ has yielded (unobservable)
$\Theta_1, \Theta_2,\ldots,\Theta_N$, and each $\Theta_i$ produces an
observation $X_i$ from an exponential family. deconvolveR is an R
package for estimating prior distribution $g(\theta)$ from the data
using Empirical Bayes deconvolution.
Details and examples may be found in the paper by Narasimhan and Efron, 2020. A vignette with further examples is also provided.