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:arXiv.org 2021-10
Main Authors: Cuevas-Pacheco, Francisco, Jean-François Coeurjolly, Marie-Hélène Descary
Format: Article
Language:English
Subjects:
Convolution
Fourier series
Mathematical models
Pattern analysis
Series expansion
Online Access:Get full text
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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 modelled as the convolution of a function \(\beta(\cdot)\), 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 \rev{can be viewed as a} log-linear model with an infinite number of coefficients, which correspond to the spectral decomposition of \(\beta(\cdot)\). 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:2331-8422