Think continuous: Markovian Gaussian models in spatial statistics

Think continuous: Markovian Gaussian models in spatial statistics

Gaussian Markov random fields (GMRFs) are frequently used as computationally efficient models in spatial statistics. Unfortunately, it has traditionally been difficult to link GMRFs with the more traditional Gaussian random field models as the Markov property is difficult to deploy in continuous space. Following the pioneering work of Lindgren et al. (2011), we expound on the link between Marko...

Gaussian Markov Random Field Models With Applications in Spatial Statistics

Gaussian Markov Random Field (GMRF) models are frequently used in statistics, and in spatial statistics in particular. The analytical properties of the Gaussian distribution are convenient and the Markov property invaluable when constructing single site Markov chain Markov Carlo algorithms. Rue (2001) demonstrates how numerical methods for sparse matrices can be utilised to construct efficient ...

Non-Gaussian and Nonparametric Models for Continuous Spatial Data

Spatial Latent Gaussian Models: Application to House Prices Data in Tehran City

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 divergenc...

Parameter Estimation in Spatial Generalized Linear Mixed Models with Skew Gaussian Random Effects using Laplace Approximation

 Spatial generalized linear mixed models are used commonly for modelling non-Gaussian discrete spatial responses. We present an algorithm for parameter estimation of the models using Laplace approximation of likelihood function. In these models, the spatial correlation structure of data is carried out by random effects or latent variables. In most spatial analysis, it is assumed that rando...