Bayesian Estimation Under Informative Sampling

• Activity Number: 478
• Type: Topic Contributed
• Date/Time: Wednesday, August 12, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Survey Research Methods Section
• Author(s): Terrance Savitsky* and Daniell Toth and Michael Sverchkov
• Companies: Bureau of Labor Statistics and Bureau of Labor Statistics and Bureau of Labor Statistics
• Keywords: Survey Sampling ; Gaussian process ; Dirichlet process ; Bayesian Hierarchical Models ; Markov chain Monte Carlo ; Consistency of Posterior Distributions

Abstract

An informative sampling design assigns probabilities of inclusion that are correlated with the response of interest and often induces a dependence among sampled observations. It is well-known that model inference performed on data acquired under an informative sampling design will be biased for estimation of the joint distribution of model parameters supposed to generate the population from which the sample was drawn. Known marginal inclusion probabilities assigned through the sampling design may be used to weight the likelihood contribution of each observed unit in the sample with the practical intent to ``undo" the design for inference about the population. This paper extends a theoretical result on consistency of the posterior distribution at the true generating distribution to the weighted ``pseudo" posterior distribution used to account for an informative sampling design. We construct conditions on known marginal and pairwise inclusion probabilities that define a class of sampling designs where consistency is achieved, in probability. The method is applied to time-indexed differences in establishment level employment counts between different survey instruments.