زهرا قیومی

Latent Gaussian models are flexible models that are applied in several statistical applications. When posterior marginals or full conditional distributions in hierarchical Bayesian inference from these models are not available in closed form, Markov chain Monte Carlo methods are implemented. The component dependence of the latent field usually causes increase in computational time and divergence of algorithms. In this paper, an integrated nested Laplace approximation is used to solve these problems, in which the Laplace approximation and the numerical integration methods are combined in an efficient way so that hard simulations are replaced by fast computation and accurate approximation. Finally the relationship between house price data, floor size, age, number of rooms, building frame, type of proprietorship and facilities such as electricity, landline, water, gas, central heating and cooling system, kitchen goods, bath and toilet are modeled by using spatial latent Gaussian models. The fitted model can be used for predicting the house price in Tehran city.

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