kppmenet: combining the kppm and elastic net regularization for inhomogeneous Cox point process with correlated covariates

Choiruddin, Achmad; Susanto, Tabita Yuni; Husain, Ahmad; Kartikasari, Yuniar Mega

doi:10.1080/02664763.2023.2207786

Cited by 8 publications

(3 citation statements)

References 30 publications

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“…Algorithm 1 still works by setting k = 1, so the model and method for a spatial (only) point process [see, e.g. 6,9,22] are covered in this study. Due to the structure of the intensity (3) and regularised likelihood (11), we perform parameter estimation for each component β k , k = 1, 2, 3 of β using a coordinate ascent algorithm [6,12], see step 2(a)-(c) of Algorithm 1.…”

Section: Variable Selection Through Regularised Likelihoodmentioning

confidence: 99%

“…. , p k , k = 1, 2, 3, where βkj are estimates obtained from maximising ( 6), (7), and (9). For comparison, we also fit the Oracle model (intensity model involving only significant covariates) to the generated 500 point patterns and estimate the parameters using maximum likelihood estimation, see ( 6), (7), and (9).…”

Section: Simulation Setupmentioning

confidence: 99%

“…Furthermore, we develop a regularisation likelihood method to perform variable selection for inhomogeneous spatio-temporal Poisson point processes with different structures of covariates (spatial, temporal, and spatio-temporal), extending the methodology developed in the purely spatial case [e.g. 1,6,9]. The flexible regularisation procedure allows different penalty functions and/or tuning parameters for each model component (spatial, temporal, or spatio-temporal).…”

Section: Introductionmentioning

confidence: 99%

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Variable selection for inhomogeneous spatio-temporal Poisson point processes

Choiruddin,

Gonz\'alez,

Mateu

et al. 2023

Preprint

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Spatio-temporal point pattern data are becoming prevalent in many scientific disciplines. We model the first-order intensity of spatio-temporal point pattern data, considering the intensity as a parametric log-linear function of spatial, temporal, and spatio-temporal covariates. Dealing with spatio-temporal covariates brings computational and methodological challenges compared to the purely spatial case. We extend regularisation methods to perform variable selection for spatial point processes to the spatio-temporal case to obtain parsimonious and more interpretable models. Using our proposed methodology, we conduct two simulation studies and examine an application to criminal activity in the Kennedy district of Bogota. In the application, we consider a spatio-temporal point pattern of crime locations and many spatial, temporal, and spatio-temporal covariates related to urban places, environmental factors, and further space-time factors. The intensity function of vehicle thefts is estimated, considering other crimes as covariate information. The proposed methodology offers a comprehensive approach for analysing spatio-temporal point pattern crime data, capturing complex relationships between covariates and crime occurrences over space and time.

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