A Bayesian Functional Data Model for Surveys Collected under Informative Sampling with Application to Mortality Estimation using NHANES

TL;DR

This paper introduces a Bayesian functional data model tailored for complex survey data, specifically addressing non-Gaussian and multivariate cases, demonstrated through mortality estimation using NHANES.

Contribution

It develops a novel Bayesian approach for functional data in survey settings, accounting for survey design and non-Gaussian data, with efficient computational techniques.

Findings

Effective mortality estimation from NHANES data

Model handles non-Gaussian and multivariate functional data

Improved inference in complex survey analysis

Abstract

Functional data are often extremely high-dimensional and exhibit strong dependence structures but can often prove valuable for both prediction and inference. The literature on functional data analysis is well developed; however, there has been very little work involving functional data in complex survey settings. Motivated by physical activity monitor data from the National Health and Nutrition Examination Survey (NHANES), we develop a Bayesian model for functional covariates that can properly account for the survey design. Our approach is intended for non-Gaussian data and can be applied in multivariate settings. In addition, we make use of a variety of Bayesian modeling techniques to ensure that the model is fit in a computationally efficient manner. We illustrate the value of our approach through an empirical simulation study as well as an example of mortality estimation using NHANES data.