Precision of stereological planar area predictors

Area of Science:

• Spatial statistics
• Geomatics
• Geographic Information Systems (GIS)

Background:

• Estimating total planar area is crucial in various scientific fields.
• Traditional methods may lack precision or efficiency in complex spatial data analysis.
• Sampling techniques offer a practical approach to area estimation.

Purpose of the Study:

• To develop and provide general formulas for approximating mean squared errors in planar area estimation using lattice sampling.
• To assess the convergence speed of these mean squared error approximations through simulations.
• To compare the performance of different sampling schemes based on approximated mean squared errors.

Main Methods:

• Utilizing lattice sampling methods, including point patterns, line segments, and quadrats.
• Deriving general formulas for mean squared error approximation.
• Developing an R package for numerical computation of the derived formulae.
• Conducting simulations to assess the speed of convergence and compare sampling schemes.

Main Results:

• Approximation formulas for mean squared errors were derived.
• The formulas are expressed as products of boundary length and a sampling-scheme-dependent parameter.
• An R package is available for computational implementation.
• Simulations demonstrated the convergence of the mean squared error approximation and allowed for scheme comparison.

Conclusions:

• The developed formulae provide a robust method for assessing the accuracy of planar area estimation via sampling.
• The R package facilitates practical application and error computation.
• The study offers insights into selecting optimal sampling schemes for accurate area estimation.