PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Bayesian Estimators for Robins-Ritov's Problem
Stefan Harmeling and Marc Toussaint
(2007) Technical Report. University of Edinburgh, School of Informatics Research Report.

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.

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EPrint Type:Monograph (Technical Report)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
ID Code:3871
Deposited By:Marc Toussaint
Deposited On:24 March 2009