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An R-Based Landscape Validation of a Competing Risk Model

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Discrete natural neighbour interpolation with uncertainty using cross-validation error-distance fields.

Thomas R Etherington¹

¹Manaaki Whenua-Landcare Research, Lincoln, New Zealand.

Peerj. Computer Science

|April 5, 2021

Summary

Natural neighbour interpolation creates accurate continuous geographic fields. A new cross-validation method quantifies uncertainty in these estimates, providing reliable error assessments for spatial analysts.

Keywords:

Convex hull Digital Neighbor Python Raster Sibson Virtual geography experiments Voronoi diagram

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Area of Science:

Geographic Information Science
Geocomputation
Spatial Analysis

Background:

Interpolation techniques are crucial for converting point data into continuous geographic fields.
Natural neighbour interpolation is a versatile method known for its exactness, smoothness, local adaptability, and lack of statistical assumptions.
Assessing the uncertainty associated with interpolated values remains a key challenge in spatial analysis.

Purpose of the Study:

To develop and validate a method for quantifying uncertainty in natural neighbour interpolation.
To create a cross-validation error-distance field to associate uncertainty with interpolated values.
To demonstrate the reliability of natural neighbour interpolation and associated error fields through virtual geography experiments.

Main Methods:

Utilized cross-validation to calculate distance-based error rates for data points.
Developed a method to generate a cross-validation error-distance field.
Conducted virtual geography experiments to test the reliability of the interpolation and error estimation methods.

Main Results:

The proposed method successfully produces a cross-validation error-distance field, associating uncertainty with natural neighbour interpolations.
Virtual geography experiments confirmed that the natural neighbour interpolation and error-distance fields provide reliable estimates within the data's convex hull.
The method is effective given an appropriate number of data points and spatial autocorrelation.

Conclusions:

The presented method offers a reliable way to assess uncertainty for natural neighbour interpolations.
This approach aids spatial analysts in understanding the reliability of their interpolated surfaces.
While not replacing expert judgment, it enhances the utility of natural neighbour interpolation for researchers.