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Empirische Inferenz Technical Report 2007

Bayesian Estimators for Robins-Ritov’s Problem

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Thumb ticker sm stefan harmeling
Empirische Inferenz
Stefan Harmeling

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.

Author(s): Harmeling, S. and Toussaint, M.
Links:
Number (issue): EDI-INF-RR-1189
Year: 2007
Month: October
Day: 0
Bibtex Type: Technical Report (techreport)
Digital: 0
Electronic Archiving: grant_archive
Institution: School of Informatics, University of Edinburgh
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

BibTex 

@techreport{6326,
  title = {Bayesian Estimators for Robins-Ritov’s Problem},
  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.},
  number = {EDI-INF-RR-1189},
  organization = {Max-Planck-Gesellschaft},
  institution = {School of Informatics, University of Edinburgh},
  school = {Biologische Kybernetik},
  month = oct,
  year = {2007},
  slug = {6326},
  author = {Harmeling, S. and Toussaint, M.},
  month_numeric = {10}
}