Bayesian functional concurrent model for missing functional data

Several functional data analysis (FDA) methods require data to be fully observed and measured regularly, with data being collected at the same fixed times for all individuals. In this study, we develop a Bayesian functional concurrent model (FCM) for function-on-function (FoF) regression which uses all of the data for modelling and can easily obtain inferences in the situation of irregular and missing data. In addition, we show that the model can be used to impute missing functional responses and/or covariates, for use by other FDA techniques. The Bayesian FCM was tested through a simulation study to compare it with other regression and imputation methods. The Bayesian model outperformed each of the other three FCMs in almost all scenarios considered. It is robust to changes in missingness, can impute missing data and allows for easy inferences through automatically generated confidence bands. The model was applied to concurrently measured functional glucose and heart dynamics, where we established a positive relationship between higher glucose and heart rhythm. Our novel Bayesian approach can estimate the FCM and impute data for fitting other FoF regression models that require fully observed data. We recommend the use of Bayesian FCM for such data.