Diverse applications using modern surveys

Disaggregated statistics help improve the description of the society. However, survey estimates are subject to larger uncertainty at finer levels than at higher levels, and often not even available at fine levels. The Behavioral Risk Factor Surveillance System (BRFSS) is considered the nation's premier system collecting health data from individuals in the US using telephone surveys. Among the BRFSS official statistics, state-level estimates are available for two related health prevalence quantities: the prevalence of having a personal doctor and the prevalence of having health insurance coverage. No county-level BRFSS estimates are released for these quantities. In addition, county-level estimates for the prevalence of having health insurance coverage are also available from the US. Small Area Health Insurance Estimates (SAHIE) program. This article addresses the disaggregation of the state-level prevalence of having a personal doctor to the county level, by using the state-level relationship between the two BRFSS prevalence variables and the county-level bridge between the BRFSS and the SAHIE prevalence of having health insurance coverage. Using 2018 public-use data, county-level model estimates are produced for both prevalence variables and on both BRFSS and SAHIE scales, improving the usability of the BRFSS public-use data. 

Human trafficking and child trafficking wreak gravely critical human rights violation. Child trafficking is a despicable form of crime inflicted upon the most vulnerable segment of the society. Reliable estimates of prevalences of child trafficking for various subpopulations is the first priority in tackling this problem. In our study, subpopulations are children aged 5-17 living in small geographic regions (or chiefdoms) in Sierra Leone. We develop improved estimates of the true rates of prevalence and identify the most adversely affected regions by estimating the unknown true ranks. These estimates shed light on the severity of the problem and bring attention to the critically affected regions (that is, chiefdoms). Using household survey data from Sierra Leone we propose a unit-level hierarchical Bayes probit regression model to reliably estimate the prevalence rates of trafficking in the chiefdoms. Using Markov chain Monte Carlo generated samples of the small area characteristics from the posterior distribution of the hierarchical Bayes model, we compute point and interval estimates of the prevalence rates, and a set of probability distributions for the unknown true ranks of the small areas in terms of their prevalence rates. 

In this article, we discuss a Bayesian Empirical Likelihood (BayesEL) based method for complex survey data leading to applications in non-probability sampling. Bayesian formulation of complex survey data presents several computational, methodological, as well as philosophical problems. Since the observations are sampled with unequal probability, the distributions of the observations in the population and the sample are different. Thus when it comes to constructing the posterior, a practioner has a choice of using one of the above distributions. Associated with this, we also need to consider if the posterior is constructed based on the sample or the whole of the finite population. This question is also related to the method used to incorporate the information in the sampling weights in the procedure. We will show that the BayesEL provides an orderly way to construct a posterior for complex survey data by addressing all the above questions. Some properties of the posterior, e.g. asymptotic validity, objective prior construction, etc will be discussed. Finally, an application to the non-probability sampling problem will be presented.