deconvolveR: A G-Modeling Program for Deconvolution and Empirical Bayes Estimation

Abstract

Empirical Bayes inference assumes an unknown prior density g(θ) has yielded (unobservables) Θ₁, Θ₂, ..., Θ_N, and each Θ_i produces an independent observation X_i from p_i (X_i | Θ_i). The marginal density f_i (X_i) is a convolution of the prior g and p_i. The Bayes deconvolution problem is one of recovering g from the data. Although estimation of g - so called g-modeling - is difficult, the results are more encouraging if the prior g is restricted to lie within a parametric family of distributions. We present a deconvolution approach where g is restricted to be in a parametric exponential family, along with an R package deconvolveR designed for the purpose.