Weighted Bayesian Bootstrap for Functional Regression

Music City Center 

Functional regression has become essential for analyzing complex, high-dimensional data collected continuously over time or space. Bayesian methods for functional regression can jointly model functional and scalar outcomes, providing straightforward construction of credible intervals. However, these methods are often limited by computational intensity and difficulties in specifying priors. We propose a Weighted Bayesian Bootstrap (WBB) approach for efficient approximate functional posterior inference by Using randomly weighted optimization of a penalized regression. We conduct an extensive simulation study to evaluate the performance of interval estimation Using the WBB approach across three functional regression models: (1) functional predictor regression, (2) functional response regression, and (3) function-on-function regression. Finally, we present an application of this approach to several real data examples.

Functional Data Analysis

Markov chain Monte Carlo

Weighted bootstrap

Functional Regression 

Section on Nonparametric Statistics