Moradi, Mohammad Mehdi
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Moradi
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Mohammad Mehdi
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Estadística, Informática y Matemáticas
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Publication Open Access Directional analysis for point patterns on linear networks(Wiley, 2021) Moradi, Mohammad Mehdi; Mateu, Jorge; Comas, Carles; Estadística, Informática y Matemáticas; Estatistika, Informatika eta MatematikaStatistical analysis of point processes often assumes that the underlying process is isotropic in the sense that its distribution is invariant under rotation. For point processes on R-2, some tests based on the K-function and nearest neighbour orientation function have been proposed to check such an assumption. However, anisotropy and directional analysis need proper caution when dealing with point processes on linear networks, as the implicit geometry of the network forces particular directions that the points of the pattern have to necessarily meet. In this paper, we adapt such tests to the case of linear networks and discuss how to use them to detect particular directional preferences, even at some angles that are different from the main angles imposed by the network. Through a simulation study, we check the performance of our proposals under different settings, over a linear network and a dendrite tree, showing that they are able to precisely detect the directional preferences of the points in the pattern, regardless the type of spatial interaction and the geometry of the network. We use our tests to highlight the directional preferences in the spatial distribution of traffic accidents in Barcelona (Spain), during 2019, and in Medellin (Colombia), during 2016.Publication Open Access Hierarchical spatio-temporal change-point detection(Taylor and Francis Group, 2023) Moradi, Mohammad Mehdi; Cronie, Ottmar; Pérez Goya, Unai; Mateu, Jorge; Estadística, Informática y Matemáticas; Estatistika, Informatika eta MatematikaDetecting change-points in multivariate settings is usually carried out by analyzing all marginals either independently, via univariate methods, or jointly, through multivariate approaches. The former discards any inherent dependencies between different marginals and the latter may suffer from domination/masking among different change-points of distinct marginals. As a remedy, we propose an approach which groups marginals with similar temporal behaviors, and then performs group-wise multivariate change-point detection. Our approach groups marginals based on hierarchical clustering using distances which adjust for inherent dependencies. Through a simulation study we show that our approach, by preventing domination/masking, significantly enhances the general performance of the employed multivariate change-point detection method. Finally, we apply our approach to two datasets: (i) Land Surface Temperature in Spain, during the years 2000–2021, and (ii) The WikiLeaks Afghan War Diary data.