Bayesian inference in multivariate spatio-temporal areal models using INLA: analysis of gender-based violence in small a
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ORIGINAL PAPER
Bayesian inference in multivariate spatio-temporal areal models using INLA: analysis of gender-based violence in small areas G. Vicente1 • T. Goicoa1,2 • M. D. Ugarte1,2,3
The Author(s) 2020
Abstract Multivariate models for spatial count data are currently receiving attention in disease mapping to model two or more diseases jointly. They have been thoroughly studied from a theoretical point of view, but their use in practice is still limited because they are computationally expensive and, in general, they are not implemented in standard software to be used routinely. Here, a new multivariate proposal, based on the recently derived M models for spatial data, is developed for spatio-temporal areal data. The model takes account of the correlation between the spatial and temporal patterns of the phenomena being studied, and it also includes spatio-temporal interactions. Though multivariate models have been traditionally fitted using Markov chain Monte Carlo techniques, here we propose to adopt integrated nested Laplace approximations to speed up computations as results obtained using both fitting techniques were nearly identical. The techniques are used to analyse two forms of crimes against women in India. In particular, we focus on the joint analysis of rapes and dowry deaths in Uttar Pradesh, the most populated Indian state, during the years 2001–2014. Keywords Crimes against women Dowry deaths Rapes Gibbs sampling Hierarchical Bayesian models INLA M-models WinBUGS
1 Introduction Crimes against women (CAW) have become a major issue in many countries due to the social concern about this form of violence that keeps women from a dignified and full life. In this context, statistical techniques in general and spatiotemporal areal models in particular can be a valuable tool to look into the spatial and temporal distribution of such form of violence. Although spatio-temporal models have been mainly applied in epidemiology to analyze chronic diseases such us cancer, some research uses these models to look for clusters of certain crimes such as burglary (see, for example Li et al. 2014). Very recently, Vicente et al. (2018, 2020) study CAW in India using univariate spatio& M. D. Ugarte [email protected] 1
Department of Statistics, Computer Science, and Mathematics, Public University of Navarre, Campus de Arrosadia, 31006 Pamplona, Spain
2
InaMat2, Public University of Navarre, Pamplona, Spain
3
Centro Asociado de la UNED, Pamplona, Spain
temporal areal data. However, the complex and multifaceted nature of the problem makes it difficult to establish relationships between certain crimes, something crucial to understand the phenomenon and to develop prevention or intervention policies. To gain knowledge about CAW, establishing relationships between different forms of crimes can set the way forward. These relationships may be expressed in terms of similar or completely different spatial and temporal patterns, that is, in terms of correlations between spatial and temporal patterns of differ
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