Bayesian Function-on-Function Regression for Spatial Functional Data

Music City Center 

Spatial functional data arise in many settings, such as particulate matter curves observed at monitoring stations and age population curves at each areal unit. Most existing functional regression models have limited applicability because they do not consider spatial correlations. Although functional kriging methods can predict the curves at unobserved spatial locations, they are based on variogram fittings rather than constructing hierarchical statistical models. We propose a Bayesian framework for spatial function-on-function regression that can carry out parameter estimations and predictions. However, the proposed model has computational and inferential challenges because the model needs to account for within and between-curve dependencies. Furthermore, high-dimensional and spatially correlated parameters can lead to the slow mixing of Markov chain Monte Carlo algorithms. To address these issues, we first utilize a basis transformation approach to simplify the covariance and apply projection methods for dimension reduction. We apply our method to both areal and point-level spatial functional data, showing the proposed method is computationally efficient and predictions.

dimension reduction

function-on-function regression

functional kriging

Markov chain Monte Carlo

Gaussian process 

Section on Bayesian Statistical Science