Modelos Gráficos Probabilísticos Aplicados al Análisis Espacial en R: Hurtos de Celulares en Bogotá

Recent technological advances enable the collection, processing and storage of information on a large scale. This has determined the beginning of big data, where the increase in information has resulted in large and complex data sets that can be potentially exploited to find solutions to relevant problems. This paper aims to explain how statistical methods can analyze these large and complex data sets, specifically spatial data. A spatial dependence analysis is performed by means of a graph that characterizes the spatial structure and a widely used model known as conditional autoregressive (CAR). These models are useful for obtaining multivariate joint distributions of a random vector based on univariate conditional specifications. These conditional specifications are based on Markov properties, so that the conditional distribution of a component of the random vector depends only on a set of neighbors, defined by the network. Conditional autoregressive models are particular cases of Markov random fields. Finally, it is explained how to perform these analyses in R, including the handling of graphs and the patterns used. Parameter estimation is performed in R following the Bayesian methodology for a data set corresponding to cell phone theft in Bogota.