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

Empirical Bayes inference assumes an unknown prior density g(θ) has yielded (unobservables) Θ1 , Θ2 , . . . , ΘN , and each Θi produces an independent observation Xi from pi (Xi |Θi ). The marginal density fi (Xi ) is a convolution of the prior g and pi . 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.