Abstract
Empirical Bayes inference assumes an unknown prior density g(θ) has yielded (unobservables) Θ<sub>1</sub>, Θ<sub>2</sub>, ..., Θ<sub>N</sub>, and each Θ<sub>i</sub> produces an independent observation X<sub>i</sub> from p<sub>i</sub> (X<sub>i</sub> | Θ<sub>i</sub>). The marginal density f<sub>i</sub> (X<sub>i</sub>) is a convolution of the prior g and p<sub>i</sub>. 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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