A convolution type model for the intensity of spatial point processes applied to eye-movement data

Estimating the first-order intensity function in point pattern analysis is an important problem, and it has been approached so far from different perspectives: parametrically, semiparametrically or nonparametrically. Our approach is close to a semiparametric one. Motivated by eye-movement data, we i...

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Bibliographic Details
Published in:Spatial statistics 2022-10, Vol.51 (3), p.100651, Article 100651
Main Authors: Coeurjolly, Jean-François, Cuevas-Pacheco, Francisco, Descary, Marie-Hélène
Format: Article
Language:English
Subjects:
Convolution
Fourier transform
Intensity function
Point processes
Statistics
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Summary:Estimating the first-order intensity function in point pattern analysis is an important problem, and it has been approached so far from different perspectives: parametrically, semiparametrically or nonparametrically. Our approach is close to a semiparametric one. Motivated by eye-movement data, we introduce a convolution type model where the log-intensity is modeled as the convolution of a function β(⋅), to be estimated, and a single spatial covariate (the image an individual is looking at for eye-movement data). Based on a Fourier series expansion, we show that the proposed model can be viewed as a log-linear model with an infinite number of coefficients, which correspond to the spectral decomposition of β(⋅). After truncation, we estimate these coefficients through a penalized Poisson likelihood. We illustrate the efficiency of the proposed methodology on simulated data and on eye-movement data.
ISSN:2211-6753
2211-6753
DOI:10.1016/j.spasta.2022.100651