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Abstract

Bayesian or likelihood-based approaches to data analysis became very popular in the field of Machine Learning. However, there exist theoretical results which question the general applicability of such approaches; among those a result by Robins and Ritov which introduce a specific example for
which they prove that a likelihood-based estimator will fail (i.e. it does for certain cases not converge to a true parameter estimate, even given infinite data). In this paper we consider various approaches to
formulate likelihood-based estimators in this example, basically by considering various extensions of the presumed generative model of the data. We can derive estimators which are very similar to the classical
Horvitz-Thompson and which also account for a priori knowledge of an observation probability function.