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

A. Sikov, J. M. Stern

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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.

Original languageEnglish
Pages (from-to)89-104
Number of pages16
JournalStatistical Papers
Issue number1
StatePublished - 15 Feb 2019
Externally publishedYes


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


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