Probabilistic Graphical Models Applied to Spatial Analysis in R: Cell Phone Thefts in Bogotá

Abstract

Recent technological advances allow large-scale collection, storage and processing information. As a consequence textbf big data has become more important nowadays, since the increase in information has given riseto large and complex data sets that can be potentially exploited to find solutions to relevant problems. Thiswork aims to explain how statistical methods can analyze these large and complex data sets, specifically spatialdata. A spatial dependency analysis is carried out by means of a graph that characterizes the spatial structureand a widely used approach known as Conditional Auto-Regressive (CAR). These models are useful for obtaining multivariate joint distributions of a random vector based on uni-variate conditional specifications. Theseconditional specifications are based on the Markov properties. Hence, that the conditional distribution of acomponent of the random vector depends only on a set of neighbors defined by the graph. CAR models areparticular cases of random Markov fields. Finally, it is explained how to carry out these analyzes in R languageprogramming including the handling of graphs and the packages used. Finally, the parameters estimation inR is carried out following the Bayesian methodology to data corresponding to stolen cell phones in BogotaColombia.