Statistics Department

 Topic:

Fully Bayesian Estimation Under Informative Sampling

Abstract:

Survey data are often collected under informative sampling designs where subject inclusion probabilities are designed to be correlated with the response variable of interest. The data modeler seeks to estimate the parameters of a population model they specify from these data. Sampling weights constructed from marginal inclusion probabilities are typically used to form an exponentiated pseudo likelihood as a plug-in estimator in a partially Bayesian pseudo posterior. We introduce the first fully Bayesian alternative, based on a Bayes rule construction, that simultaneously performs weight smoothing and estimates the population model parameters in a construction that treats the response variable(s) and inclusion probabilities as jointly randomly generated from a population distribution.

We compare performances between the two approaches on synthetic data. We demonstrate that the credibility intervals under our fully Bayesian method achieve nominal coverage. As an example, we apply our method to data from the National Health and Nutrition Examination Survey (NHANES) to explore the relationship between caffeine consumption and systolic blood pressure.

 For more information about Luis Leon-Novelo, Ph.D. , click here.