Multivariate Kalman filtering for spatio-temporal processes.

An increasing interest in models for multivariate spatio-temporal processes has been noted in the last years. Some of these models are very flexible and can capture both marginal and cross spatial associations amongst the components of the multivariate process. In order to contribute to the statistical analysis of these models, this paper deals with the estimation and prediction of multivariate spatio-temporal processes by using multivariate state-space models. In this context, a multivariate spatio-temporal process is represented through the well-known Wold decomposition. Such an approach allows for an easy implementation of the Kalman filter to estimate linear temporal processes exhibiting both short and long range dependencies, together with a spatial correlation structure. We illustrate, through simulation experiments, that our method offers a good balance between statistical efficiency and computational complexity. Finally, we apply the method for the analysis of a bivariate dataset on average daily temperatures and maximum daily solar radiations from 21 meteorological stations located in a portion of south-central Chile. Supplementary Information: The online version contains supplementary material available at 10.1007/s00477-022-02266-3.

A Spatially Correlated Model with Generalized Autoregressive Conditionally Heteroskedastic Structure for Counts of Crimes.

Crime is a negative phenomenon that affects the daily life of the population and its development. When modeling crime data, assumptions on either the spatial or the temporal relationship between observations are necessary if any statistical analysis is to be performed. In this paper, we structure space-time dependency for count data by considering a stochastic difference equation for the intensity of the space-time process rather than placing structure on a latent space-time process, as Cox processes would do. We introduce a class of spatially correlated self-exciting spatio-temporal models for count data that capture both dependence due to self-excitation, as well as dependence in an underlying spatial process. We follow the principles in Clark and Dixon (2021) but considering a generalized additive structure on spatio-temporal varying covariates. A Bayesian framework is proposed for inference of model parameters. We analyze three distinct crime datasets in the city of Riobamba (Ecuador). Our model fits the data well and provides better predictions than other alternatives.

A spatial randomness test based on the box-counting dimension.

Statistical modelling of a spatial point pattern often begins by testing the hypothesis of spatial randomness. Classical tests are based on quadrat counts and distance-based methods. Alternatively, we propose a new statistical test of spatial randomness based on the fractal dimension, calculated through the box-counting method providing an inferential perspective contrary to the more often descriptive use of this method. We also develop a graphical test based on the log-log plot to calculate the box-counting dimension. We evaluate the performance of our methodology by conducting a simulation study and analysing a COVID-19 dataset. The results reinforce the good performance of the method that arises as an alternative to the more classical distances-based strategies.

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.

Spatial generalised linear mixed models based on distances.

Risk models derived from environmental data have been widely shown to be effective in delineating geographical areas of risk because they are intuitively easy to understand. We present a new method based on distances, which allows the modelling of continuous and non-continuous random variables through distance-based spatial generalised linear mixed models. The parameters are estimated using Markov chain Monte Carlo maximum likelihood, which is a feasible and a useful technique. The proposed method depends on a detrending step built from continuous or categorical explanatory variables, or a mixture among them, by using an appropriate Euclidean distance. The method is illustrated through the analysis of the variation in the prevalence of Loa loa among a sample of village residents in Cameroon, where the explanatory variables included elevation, together with maximum normalised-difference vegetation index and the standard deviation of normalised-difference vegetation index calculated from repeated satellite scans over time.

Spatio-temporal modeling of benthic biological species.

The spatial and temporal distribution of the number of benthic species located in an important area under ecological stress (Puerto CALICA, Quintana Roo, Mexico) is analyzed by means of Gaussian Spatial Linear Mixed Models. Following a model-based approach we derive spatial predictions taking into account temporal variations between May 1996 and June 1999. The proposed models were evaluated in terms of their ability to detect the underlying spatial structure for further interpolation. Uncertainty in the prediction could be evaluated by using the Bayesian paradigm. The results can be used as a guide for further environmental management policies in the region.

Neoplasia oclusiva de colon / Colonic occlusive neoplasms

Desde diciembre 1987 a mayo 1992 se operaron 50 pacientes con obstrucción neoplásica de colon. La sintomatología aguda más frecuente que presentaron fue: dolor abdominal en el 86 por ciento, distensión abdominal en el 76 por ciento y falta de eliminación de gases en 56 por ciento. Los pacientes exhibían como antecedentes: alteraciones del ritmo evacuatorio, anemia y protorragía en 76,36 y 12 por ciento respectivamente. 78 por ciento de los pacientes fue operado dentro de las 24 horas de su ingreso al servicio. La decisión quirúrgica fue tomada por la clínica y la radiología simple de abdomen en 60 por ciento de los casos, efectuandose un estudio colónico contrastado en el 40 por ciento , de los cuales, para llegar al dignóstico, un 40 por ciento requirió además un estudio endoscópico. Estos estudios efectuados de acuerdo a la urgencia que presentó el paciente. La localización de la neoplasia fue colon sigmoides 42 por ciento, descedente y ángulo esplénico 20 por ciento, colon derecho 14 por ciento, transverso 14 por ciento y recto 12 por ciento. El tratamiento quirúrgico efectuado fue en el 68 por ciento de los casos, la reseción, teniendo un 36 por ciento de operaciones Hartmann, 14 por ciento hemicolectomías derechas, 8 por ciento de otros tipos de operaciones resectivas, 4 por ciento de operaciones Lahey, 2 por ciento de colectomías subtotales y 2 por ciento de polipectomías. El 32 por ciento de los pacientes no fueron resecados y se efectuaron derivaciones externas en el 26 por ciento e internas en el 6 por ciento. La morbilidad y mortalidad son comparables a la internacionales del 22 y 10 por ciento respectivamente. Concluimos que la intervención quirúrgica más adecuada es la que efectua la ectomía del tumor

Neoplasia oclusiva de colon / Colonic occlusive neoplasms

Desde diciembre 1987 a mayo 1992 se operaron 50 pacientes con obstrucción neoplásica de colon. La sintomatología aguda más frecuente que presentaron fue: dolor abdominal en el 86 por ciento, distensión abdominal en el 76 por ciento y falta de eliminación de gases en 56 por ciento. Los pacientes exhibían como antecedentes: alteraciones del ritmo evacuatorio, anemia y protorragía en 76,36 y 12 por ciento respectivamente. 78 por ciento de los pacientes fue operado dentro de las 24 horas de su ingreso al servicio. La decisión quirúrgica fue tomada por la clínica y la radiología simple de abdomen en 60 por ciento de los casos, efectuandose un estudio colónico contrastado en el 40 por ciento , de los cuales, para llegar al dignóstico, un 40 por ciento requirió además un estudio endoscópico. Estos estudios efectuados de acuerdo a la urgencia que presentó el paciente. La localización de la neoplasia fue colon sigmoides 42 por ciento, descedente y ángulo esplénico 20 por ciento, colon derecho 14 por ciento, transverso 14 por ciento y recto 12 por ciento. El tratamiento quirúrgico efectuado fue en el 68 por ciento de los casos, la reseción, teniendo un 36 por ciento de operaciones Hartmann, 14 por ciento hemicolectomías derechas, 8 por ciento de otros tipos de operaciones resectivas, 4 por ciento de operaciones Lahey, 2 por ciento de colectomías subtotales y 2 por ciento de polipectomías. El 32 por ciento de los pacientes no fueron resecados y se efectuaron derivaciones externas en el 26 por ciento e internas en el 6 por ciento. La morbilidad y mortalidad son comparables a la internacionales del 22 y 10 por ciento respectivamente. Concluimos que la intervención quirúrgica más adecuada es la que efectua la ectomía del tumor