Spatial Gaussian Markov Random Fields: Modelling, Applications and Efficient Computations

Efficient Computations for Gaussian Markov Random Field Models with two Applications in Spatial Epidemiology

Gaussian Markov random fields (GMRFs) 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 Monte Carlo algorithms. Rue (2001) demonstrates how numerical methods for sparse matrices can be utilised to construct efficient algori...

Gaussian Markov Random Fields: Theory and Applications

Transformed Gaussian Markov Random Fields and 1 Spatial Modeling

15 The Gaussian random field (GRF) and the Gaussian Markov random field (GMRF) have 16 been widely used to accommodate spatial dependence under the generalized linear mixed 17 model framework. These models have limitations rooted in the symmetry and thin tail of the 18 Gaussian distribution. We introduce a new class of random fields, termed transformed GRF 19 (TGRF), and a new class of Markov r...

Modelling Gaussian Fields and Geostatistical Data Using Gaussian Markov Random Fields

NORGES TEKNISK-NATURVITENSKAPELIGE UNIVERSITET Modelling spatial variation in disease risk using Gaussian Markov random field proxies for Gaussian random fields

Analyses of spatial variation in disease risk based on area-level summaries of disease counts are most often based on the assumption that the relative risk is uniform across each region. Such approaches introduce an artificial piecewise-constant relative risk-surface with discontinuities at regional boundaries. A more natural approach is to assume that the spatial variation in risk can be repre...