Randomized Bayesian Quadrature for Stereological Estimation with Spatial Point Process Sampling

F. J. Soto

Stereological estimation uses systematic random sampling to estimate quantities such as particle counts, lengths, areas, and volumes. The classical Cavalieri method works with parallel sections, but other designs, such as punch biopsies, involve one-dimensional fibers and locations with two degrees of freedom. In practice, irregular spacing and measurement error make these designs harder to analyze and naturally lead to spatial point process models. We study this problem through numerical integration, with special attention to statistical estimation, sampling variability, and variance control under mild assumptions, for instance stationarity at fixed intensity. The main goal is to understand how randomized Bayesian quadrature rules behave in this setting and to strengthen their theoretical basis for stereological applications.

Keywords: stereology, spatial point processes, Bayesian quadrature

Functional Data Analysis, Spatial and Spatio-Temporal Statistics
September 2, 2026  5:40 PM
Aula 26

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