Bayesian weighted inference from surveys

David Gunawan, Anastasios Panagiotelis, William Griffiths, Duangkamon Chotikapanich

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Abstract

Data from large surveys are often supplemented with sampling weights that are designed to reflect unequal probabilities of response and selection inherent in complex survey sampling methods. We propose two methods for Bayesian estimation of parametric models in a setting where the survey data and the weights are available, but where information on how the weights were constructed is unavailable. The first approach is to simply replace the likelihood with the pseudo likelihood in the formulation of Bayes theorem. This is proven to lead to a consistent estimator but also leads to credible intervals that suffer from systematic undercoverage. Our second approach involves using the weights to generate a representative sample which is integrated into a Markov chain Monte Carlo (MCMC) or other simulation algorithms designed to estimate the parameters of the model. In the extensive simulation studies, the latter methodology is shown to achieve performance comparable to the standard frequentist solution of pseudo maximum likelihood, with the added advantage of being applicable to models that require inference via MCMC. The methodology is demonstrated further by fitting a mixture of gamma densities to a sample of Australian household income.

Original languageEnglish
Pages (from-to)71-94
Number of pages23
JournalAustralian & New Zealand Journal of Statistics
Volume62
Issue number1
DOIs
Publication statusPublished - Apr 2020

Keywords

  • gamma mixture
  • latent representative sample
  • Markov chain Monte Carlo
  • pseudo maximum likelihood
  • sampling weights

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