Bayesian Spatio-Temporal Modeling for Analysing Local Patterns of Crime Over Time at the Small-Area Level

Assessing trends and seasonal changes in elephant poaching risk at the small area level using spatio-temporal Bayesian modeling

“…δ i is the interaction between the spatial and temporal effects. To explore the geographic variation of the local trends, we mapped the posterior probability (PP) of a local differential trend (δ i ) that was greater than the mean trend (Law et al 2014. PP can be viewed as the Bayesian equivalent of the p-value (Meng and Dempster 1987).…”

“…A normal distribution prior with mean 0 and variance σ s 2 was specified for u i . The prior for the regional time trend (ƴ) was a vague prior normal distribution with mean equal to zero and variance of 1000 (Law et al 2014). An Intrinsic Conditional Autoregressive Gaussian distribution (ICAR) was used to specify priors for spatial random effect s i and spatio-temporal interaction δ i (Torabi and Rosychuk 2012, Law et al 2014, 2015, Li et al 2014, Luan et al 2015.…”

“…The prior for the regional time trend (ƴ) was a vague prior normal distribution with mean equal to zero and variance of 1000 (Law et al 2014). An Intrinsic Conditional Autoregressive Gaussian distribution (ICAR) was used to specify priors for spatial random effect s i and spatio-temporal interaction δ i (Torabi and Rosychuk 2012, Law et al 2014, 2015, Li et al 2014, Luan et al 2015. Under the ICAR specification, the means of s i and δ i for one block depend on the s i and δ i , respectively, of the neighboring blocks' distribution, where adjacency is defined as areas that have common borders (Torabi andRosychuk 2012, Luan et al 2015).…”

“…Under the ICAR specification, the means of s i and δ i for one block depend on the s i and δ i , respectively, of the neighboring blocks' distribution, where adjacency is defined as areas that have common borders (Torabi andRosychuk 2012, Luan et al 2015). The amount of variation of s i and δ i is controlled by hyperparameters σ s 2 and σ δ 2 , respectively, and is contrariwise related to the number of neighbors of the ith block (Torabi and Rosychuk 2012, Law et al 2014, 2015, Li et al 2014, Luan et al 2015. In Bayesian approaches, priors assigned to hyperparameters (i.e.…”

“…For each model, to obtain 20,000 samples from the posterior distribution, MCMC chains comprising 10,000 iterations with a burn-in of 1000 were found to be sufficient to achieve convergence. Convergence was assessed by Brook-Gelman-Rubin Diagnostic, history plots, visually examining trace plots and Monte Carlo standard error (<5 % of the sample posterior standard deviation) (Law et al 2014, Luan et al 2015.…”