Bayesian Weighted Inference from Surveys "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 embedded within a Markov chain Monte Carlo (MCMC) or other simulation algorithm designed to estimate the parameters of the model. In 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."

Gunawan, David; Griffths, William; Anatasios Panagiotelis and Duangkamon Chotikapanich

Bayesian Weighted Inference from Surveys "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 embedded within a Markov chain Monte Carlo (MCMC) or other simulation algorithm designed to estimate the parameters of the model. In 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."

David Gunawan, William Griffths () and Anatasios Panagiotelis and Duangkamon Chotikapanich
Additional contact information
David Gunawan: University of New South Wales
William Griffths: Department of Economics, The University of Melbourne, https://www.findanexpert.unimelb.edu.au/display/person7036
Anatasios Panagiotelis and Duangkamon Chotikapanich: Monash University
Authors registered in the RePEc Author Service: Anastasios Nicholas Panagiotelis

Department of Economics - Working Papers Series from The University of Melbourne

Keywords: Sampling weights; Latent representative sample; Markov chain Monte Carlo; Gamma mixture; Pseudo maximum likelihood. (search for similar items in EconPapers)
Pages: 38 pages
Date: 2017-03
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