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This research aims to enhance the selection of cubature parameters for accurate inference in three-dimensional Poisson point processes.

Recommendations on cubature parameter selection for likelihood approximation in three-dimensional Poisson point processes

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Recommendations improve likelihood approximation in Poisson point processes, suggesting better inference accuracy.

This research aims to enhance the selection of cubature parameters for accurate inference in three-dimensional Poisson point processes.
Formalized a cubature scheme in three-dimensional space (R3)
Conducted extensive simulations across various Poisson scenarios and cubature configurations
Evaluated cubature settings using mean squared error and diagnostic tests for performance.
Identified optimal dummy-point ratio and tessellation resolution for stable estimates
Demonstrated improved reliability of fitted intensities and diagnostics
Provided practical recommendations based on simulation outcomes.

Tarantino et al. (2026) studied this question.

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