A generalized Tweedie identity and moment-generating-function representation enable nonparametric recovery of full posteriors for heteroscedastic normal means with unknown variances without specifying a prior.
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Nonparametric f-Modeling for Empirical Bayes Inference with Unequal and Unknown Variances
A generalized Tweedie identity and moment-generating-function representation enable nonparametric recovery of full posteriors for heteroscedastic normal means with unknown variances without specifying a prior.