BAMIFun: Bayesian Multiple Imputation for Functional Data

2026-05-08

AI Summary

This study addresses the challenge of missing data in functional datasets arising from sparse or irregular observations, which often leads to overly optimistic inferences in downstream analyses when using single imputation methods. To overcome this limitation, we propose BAMIFun, the first Bayesian multiple imputation framework tailored for functional data. BAMIFun integrates low-rank penalized spline representations with efficient Gibbs sampling to produce smooth, uncertainty-aware imputations. We further extend this framework to multi-way functional data by introducing Functional Tensor Singular Value Decomposition (FTSVD), enabling effective handling of complex missingness patterns. Empirical evaluations demonstrate that BAMIFun substantially improves imputation accuracy, achieves better coverage of confidence intervals, and enhances the reliability of subsequent statistical inferences.

Abstract

Missing data are pervasive in modern functional datasets, where trajectories are often sparsely or irregularly observed. Although Functional Principal Component Analysis (FPCA) is widely used to reconstruct incomplete curves, existing FPCA-based approaches typically employ single imputation, leading to overly optimistic inferences in downstream analyses. To address these challenges, we develop a novel Bayesian multiple imputation framework for functional data (BAMIFun). For single-level functional data, we impose a Bayesian low-rank model that incorporates penalized spline representations to enforce smoothness of eigenfunctions and derive an efficient Gibbs sampler algorithm for posterior computation. In addition, we demonstrate and validate how to properly account for the estimation uncertainties in downstream analysis. Furthermore, we extend the framework to multiway functional data using a low-rank Functional Tensor Singular Value Decomposition (FTSVD) model, enabling Bayesian multiple imputation in settings not supported by existing methods. Simulation studies show that, compared to existing methods, BAMIFun achieves accurate imputation while providing substantially improved coverage and more reliable downstream inference. Case studies using a physical activity dataset and an infant gut microbiome dataset further demonstrate the practical advantages of our proposed methods under severe missingness. Code for our algorithms is available at https://github.com/ZirenJiang/BAMIFun.

Problem

• missing data
• functional data
• multiple imputation
• Bayesian inference
• uncertainty quantification

Innovation

• Bayesian multiple imputation
• Functional data
• Low-rank model
• Penalized splines
• Functional Tensor SVD