Research Projects

Large-scale national surveys, vital for policy in economics and public health, employ complex multi-stage designs (stratification, clustering, unequal selection probabilities) which violate the independent and identically distributed (IID) assumption, leading to biased estimates if sampling is informative and underestimated variances. While classical survey estimation methods suffice for large regions, they fail for "small areas" due to sparse samples, resulting in imprecise estimates. Although Bayesian Hierarchical Models (BHMs) offer flexibility for Small Area Estimation (SAE), they face significant challenges: they can become exceedingly complex with thousands of poststratification cells, especially when modeling interactions, leading to unstable or uninterpretable estimates. Additionally, there's limited guidance on incorporating continuous covariates and non-trivial interpretation and application of survey weights, particularly for non-linear models where simple weighted averages break down. This research aims to address these critical limitations. The research aims to develop novel Bayesian computational approaches to advance regression modeling for complex multi-stage survey data. The primary objective is to create principled Bayesian computational methods for integrating survey weights and design effects, especially those incorporating nonparametric approaches like smoothing splines. The study will compare existing as well as novel approaches in terms of precision estimation (Mean Squared Error (MSE), Mean Absolute Deviation (MAD), etc.), via real world examples as well as simulation models that accurately reflect various sources of uncertainty from complex survey designs. The central hypothesis is that these advanced Bayesian frameworks can integrate complex survey design features, overcoming current challenges. The research will employ a combination of theoretical development, simulation studies, and practical application to real world examples. Theoretical work is required to formalise novel Bayesian hierarchical models that incorporate continuous predictors. Previous work suggests that these models should be nonparametric in nature, making the development of suitable models challenging. Extensive simulations, potentially using subsamples of actual surveys (e.g., NHANES), will be required to evaluate the bias, variance, and efficiency of proposed methods versus existing ones under various scenarios. We hope to apply the developed methods to real-world data from the NHANES survey, a rich public-use epidemiological dataset where estimating health outcomes for small subpopulations, accounting for multi-stage clustering and continuous covariates is highly pertinent. We also hope to apply the methods to the rich and complex national survey data collected in India. In addition to new theoretical frameworks for robust Bayesian regression models for complex multi-stage survey data, we expect to develop a useful computational framework, which will be implemented in suitable open source computational environments (e.g., R, Stan, PyMC) to ensure accessibility.