Functional CAR models for large spatially correlated functional datasets.

Area of Science:

• Statistics
• Spatial Statistics
• Functional Data Analysis

Background:

• Spatially correlated data with functional responses present unique analytical challenges.
• Existing models often struggle with nonseparable and nonstationary covariance structures in both space and function domains.
• Accurate modeling is crucial for fields like genomics and image analysis.

Purpose of the Study:

• To develop a novel functional conditional autoregressive (CAR) model for spatially correlated functional data.
• To account for complex spatial correlations, including nonseparable and nonstationary covariance structures.
• To improve functional regression performance and identify novel spatial patterns in data.

Main Methods:

• Developed a functional CAR model for areal lattice data with functional responses.
• Incorporated nonseparable and nonstationary covariance structures in spatial and functional domains.
• Utilized basis transformation strategies for computational scalability and generalization to higher dimensions.

Main Results:

• The model theoretically demonstrates CAR properties at each functional location with varying spatial covariance parameters.
• Basis transformation strategies ensure computational scalability for large functional datasets and generalization to various basis functions.
• Simulation studies confirm improved functional regression performance when spatial correlation is accounted for.

Conclusions:

• The proposed functional CAR model effectively handles complex spatial-functional dependencies.
• The model offers computational advantages and broad applicability, including to image data.
• Application to copy number data revealed genetic markers missed by methods ignoring spatial correlations, highlighting its utility in high-throughput biological studies.