Statistical Papers

, Volume 60, Issue 1, pp 89–104 | Cite as

Application of the full Bayesian significance test to model selection under informative sampling

  • A. SikovEmail author
  • J. M. Stern
Regular Article


Adopting likelihood based methods of inference in the case of informative sampling often presents a number of difficulties, particularly, if the parametric form of the model that describes the sample selection mechanism is unknown, and thus requires application of some model selection approach. These difficulties generally arise either due to complexity of the model holding in the sample, or due to identifiability problems. As a remedy we propose alternative approach to model selection and estimation in the case of informative sampling. Our approach is based on weighted estimation equations, where the contribution to the estimation equation from each observation is weighted by the inverse probability of being selected. We show how weighted estimation equations can be incorporated in a Bayesian analysis, and how the full Bayesian significance test can be implemented as a model selection tool. We illustrate the efficiency of the proposed methodology by a simulation study.


Informative sampling Design variables Inclusion probability Bayesian significance measures Horvitz–Thompson estimator Population distribution Sample distribution 



The authors are grateful for the support of IME-USP, the Institute of Mathematics and Statistics of the University of São Paulo; FAPESP - the State of São Paulo Research Foundation (grant CEPID 2013/07375-0 and 2013/17746-5); and CNPq - the Brazilian National Counsel of Technological and Scientific Development (grant PQ 301206/2011-2). Finally, the authors are grateful for the advice of colleagues and anonymous referees used to improve this work.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Institute of Mathematics and StatisticsUniversity of Sao Paulo (IME-USP)São PauloBrazil

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