Bayesian Function-on-Function Regression for Spatial Functional Data
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...
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Zusammenfassung: | 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.
In this manuscript, 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 also
develop a simultaneous band score for the proposed model to detect the
significant region in the regression function. We apply our method to both
areal and point-level spatial functional data, showing the proposed method is
computationally efficient and provides accurate estimations and predictions. |
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DOI: | 10.48550/arxiv.2401.08175 |