Spatial Analysis of Structured Additive Regression and Modeling of Crime Data in Tehran City Using Integrated Nested Laplace Approximation

In Bayesian analysis of structured additive regression models which are a flexible class of statistical models، the posterior distributions are not available in a closed form، so Markov chain Monte Carlo algorithm due to complexity and large number of hyperparameters takes long time. Integrated nested Laplace approximation method can avoid the hard simulations using the Gaussian and Laplace approximations. In this paper، consideration of spatial correlation of the data in structured additive regression model and its estimation by the integrated nested Laplace approximation are studied. Then a crime data set in Tehran city are modeled and evaluated. Next، a simulation study is performed to compare the computational time and precision of the models provided by the integrated nested Laplace approximation and Markov chain Monte Carlo algorithm