empirical-bayes-confidence-intervals-paper

A repository for reproducing the numerical results in the following paper:

Ignatiadis, Nikolaos, and Stefan Wager. "Confidence Intervals for Nonparametric Empirical Bayes Analysis." Journal of the American Statistical Association: Theory and Methods (2022)

A preprint is also available at arXiv:1902.02774.

See Empirikos.jl for the Julia package implementing the proposed method.

Please see the `rejoinder' folder for code reproducing the rejoinder for the JASA discussion of the above paper.

File description

• Setup: Manifest.toml and Project.toml, specifications of Julia packages used.
• Real data examples: bichsel.jl, lord_cressie.jl and prostate.jl reproduce the three real data examples of the paper (Figure 1, Figure 2 and Table 2). These examples have been implemented as Pluto.jl notebooks.
• Simulations:
  • simulation_ebci.jl: Main script for running simulations. It can be called for example as julia -t 10 simulation_ebci.jl postmean negspiky where 10 is the number of threads. See the _simulation_*.sbatch files for all the calls of this script reported in the manuscript.
  • simulation_expfamily.jl: Script to run simulations with Logspline and varying degrees of freedom.
  • simulation_plots.jl: Takes the output of the simulation scripts above and generates Figures 3-7 of the paper .
  • asymptotic_ci_length.jl: Code for Figure 8 of the paper.

Requirements and version-info for reproduction

• The Mosek convex programming solver, version 9.2, was used in the simulations. Mosek requires a license (there is an option for a free academic license).
• Julia version 1.6.2.
• All required Julia packages and their versions are specified in Project.toml and Manifest.toml. They may be installed automatically by starting a Julia session in this folder and typing:

using Pkg
Pkg.activate(".")
Pkg.instantiate()

Repository history

• Version 2 of this manuscript on arXiv (arXiv:1902.02774v2) was substantially different. See this repository at the arXiv_V2 release tag to reproduce the results of that version.
• Similarly, you can find the code for version 3 (arXiv:1902.02774v3) at the arXiv_V3 release tag.