Effective Sample Size for Functional Spatial Data

2026-01-28

AI Summary

This study addresses the issue of information redundancy in functional spatial data arising from observational dependence by extending the concept of effective sample size (ESS) to the domain of functional geostatistics for the first time. By introducing the trace variogram to characterize inter-functional correlation structures and integrating functional autoregressive modeling with eigen-decomposition, the authors formulate a novel ESS definition that preserves the intuitive properties of its classical scalar counterpart. This framework elucidates how serial dependence and variability along eigen-directions jointly influence ESS. Empirical evaluation on real meteorological data—specifically, geometric vertical velocity curves over a localized region—demonstrates that the proposed method effectively quantifies redundant information and accurately estimates the effective number of independent functional observations.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

The effective sample size quantifies the amount of independent information contained in a dataset, accounting for redundancy due to correlation between observations. While widely used in geostatistics for scalar data, its extension to functional spatial data has remained largely unexplored. In this work, we introduce a novel definition of the effective sample size for functional geostatistical data, employing the trace-covariogram as a measure of correlation, and show that it retains the intuitive properties of the classical scalar ESS. We illustrate the behavior of this measure using a functional autoregressive process, demonstrating how serial dependence and the allocation of variability across eigen-directions influence the resulting functional ESS. Finally, the approach is applied to a real meteorological dataset of geometric vertical velocities over a portion of the Earth, showing how the method can quantify redundancy and determine the effective number of independent curves in functional spatial datasets.

Problem

• effective sample size
• functional spatial data
• trace-covariogram
• geostatistics
• information redundancy

Innovation

• effective sample size
• functional spatial data
• trace-covariogram
• functional geostatistics
• eigen-direction variability