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

Balasubramanian Narasimhan, Bradley Efron

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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.

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