Bounding uncertainty in functional data: A case study

Abstract

Functional data are fast becoming a preeminent source of information across a wide range of industries. A particularly challenging aspect of functional data is bounding uncertainty. In this unique case study, we present our attempts at creating bounding functions for selected applications at Sandia National Laboratories (SNL). The first attempt involved a simple extension of functional principal component analysis (fPCA) to incorporate covariates. Though this method was straightforward, the extension was plagued by poor coverage accuracy for the bounding curve. This led to a second attempt utilizing elastic methodology which yielded more accurate coverage at the cost of more complexity.