Empirikos
ἐμπειρικός: “experienced” in ancient Greek, etymology of empirical
Empirical Bayes estimation and inference in Julia.
Consider \(n\) independent samples \(Z_i\) drawn from the following hierarchical model \[ \mu_i \sim G, \ \ Z_i \sim p_i(\cdot \mid \mu_i). \] Here \(G\) is the unknown prior (effect size distribution) and \(p_i(\cdot \mid \mu_i),i=1,\dotsc,n\) are known likelihood functions.
This package provides a unified framework for estimation and inference under the above setting, which is known as the empirical Bayes problem (Robbins 1956).
Installation
The package is available from the Julia registry. It may be installed on Julia version 1.10 as follows:
using Pkg
Pkg.add("Empirikos")For some of its functionality, this package requires a convex programming solver. The requirement for such a solver is that it can solve second order conic programs (SOCP), that it returns the dual variables associated with the SOCP constraints and that it is supported by JuMP.jl. We recommend using the MOSEK solver through the MosekTools.jl package. MOSEK is a commercial solver, but provides free academic licenses. An open-source alternative is Hypatia.jl.
This package has been designed with the goal of modularity. Specialized code (using Julia’s multiple dispatch) can be easily added to more efficiently handle different combinations of estimation targets, statistical algorithms, classes of priors and likelihoods. Please open an issue if there is a combination thereof that you would like to use (and which does not work currently or is slow).
References