Erratum and remarks on "Nonparametric posterior learning for emission tomography"
Résumé
In this text we provide two remarks to the article "Nonparametric posterior learning for emission tomographies", F. Goncharov, et. al. (2021): correction of one mistake and an additional theorem on existence of conjectured estimator. First, a mistake was made when inferring fully nonparametric posterior distribution on point processes in the original work. Here we obtain the correct expression and notice that it leads to an unwanted bias in assigned intensities for sampled Poisson processes. The bias seems less harmful in finite-dimensions, but in fully-nonparametric regime it makes the model inadequate for the task. In view of this, the mistake being made in the original work can be seen as reasonable correction of bad prior elicitation. This result serves also a reminder for being careful when eliciting nonparametric priors for sampling algorithms such as Nonparametric Posterior Learning (NPL), Weighted Bayesian Bootstrap (WBB), Weighted Likelihood boostrap (WLB). Secondly, we provide explicit construction of the conjectured estimator under assumption of correct model specification which finally grounds original theoretical studies of the model of NPL for emission tomographies.
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