Point patterns occurring on complex structures in space and space-time: An alternative network approach

This paper presents an alternative approach of analyzing possibly multitype point patterns in space and space-time that occur on network structures, and introduces several different graph-related intensity measures. The proposed formalism allows to control for processes on undirected, directional as well as partially directed network structures and is not restricted to linearity or circularity

Statistical procedures for spatial point pattern recognition

Spatial structures in the form of point patterns arise in many different contexts, and in most of them the key goal concerns the detection and recognition of the underlying spatial pattern. Particularly interesting is the case of pattern analysis with replicated data in two or more experimental groups. This paper compares design-based and model-based approaches to the analysis of this kind of spatial data. Basic questions about pattern detection concern estimating the properties of the underlying spatial point process within each experimental group, and comparing the properties between groups. The paper discusses how either approach can be implemented in the specific context of a single-factor replicated experiment and uses simulations to show how the model-based approach can be more efficient when the underlying model assumptions hold, but potentially misleading otherwise

Wavelet-Based Entropy Measures to Characterize Two-Dimensional Fractional Brownian Fields

The aim of this work was to extend the results of Perez et al. (Physica A (2006), 365 (2), 282–288) to the two-dimensional (2D) fractional Brownian field. In particular, we defined Shannon entropy using the wavelet spectrum from which the Hurst exponent is estimated by the regression of the logarithm of the square coefficients over the levels of resolutions. Using the same methodology. we also defined two other entropies in 2D: Tsallis and the Rényi entropies. A simulation study was performed for showing the ability of the method to characterize 2D (in this case, α = 2) self-similar processes

Testing similarity between first-order intensities of spatial point processes. A comparative study

Testing whether two spatial point processes have the same spatial distribution is an important task that can be addressed from different perspectives. A Kolmogorov-Smirnov test with asymptotic calibration and a Cramer von Mises type test with bootstrap calibration have recently been developed to compare the first-order intensity of two observed patterns. Motivated by common practice in epidemiological studies, we introduce a regression test based on the relative risk function with two alternative bootstrap calibrations. This paper compares the performance of these nonparametric tests through both an intensive simulation study, and the application to wildfire and crime data. The three tests provide good calibrations of the null hypothesis for simulated Poisson and non-Poisson spatial point processes, but the Cramer von Mises and regression tests outperform the cost-efficient Kolmogorov-Smirnov test in terms of power. In the real data analysis we have seen that the Kolmogorov-Smirnov test does not detect differences between spatial point patterns when dealing with sparse data. In view of these results, it would be preferable using the Cramer von Mises or regression tests despite their higher computational demand

Detección de rasgos en imágenes binarias mediante procesos puntuales espaciales marcados

En este trabajo consideramos el problema de la detección de rasgos bajo la presencia de ruido en imágenes que tras un cierto tratamiento se reducen a binarias, por la presencia de dos tipos de elementos. Podemos encontrar ejemplos de este problema en la detección de minas por medio de imágenes de avión o satélite, en la búsqueda de rasgos en imágenes microscópicas de células, o en la caracterización de fallas en zonas de terremotos. En primer lugar revisamos algunos métodos de detección jerárquicos basados en modelos probabilísticos, en los que los rasgos proceden de distribuciones normales multivariantes y el ruido surge según un proceso de Poisson espacial. Posteriormente, presentamos una nueva solución al problema mediante el uso de procesos puntuales espaciales marcados. Definimos un proceso puntual marcado en el que a cada localización se le asigna un par de marcas: las distancias al K-ésimo vecino más cercano y una variable dicotómica diferenciadora del rasgo frente al ruido. Esas distancias se modelizan como una mixtura de distribuciones cuyos parámetros se determinan mediante el algoritmo EM. Finalmente la nueva metodología es evaluada y contrastada sobre simulaciones y casos reales

Second-order preserving point process permutations

While random permutations of point processes are useful for generating counterfactuals in bivariate interaction tests, such permutations require that the underlying intensity be separable. In many real-world datasets where clustering or inhibition is present, such an assumption does not hold. Here, we introduce a simple combinatorial optimization algorithm that generates second-order preserving (SOP) point process permutations, for example, permutations of the times of events such that the function of the permuted process matches the function of the data. We apply the algorithm to synthetic data generated by a self-exciting Hawkes process and a self-avoiding point process, along with data from Los Angeles on earthquakes and arsons and data from Indianapolis on law enforcement drug seizures and overdoses. In all cases, we are able to generate a diverse sample of permuted point processes where the distribution of the functions closely matches that of the data. We then show how SOP point process permutations can be used in two applications: (1) bivariate Knox tests and (2) data augmentation to improve deep learning-based space-time forecasts