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Coming up with Bayesian models for spatial data is easy, but performing inference with them can be challenging. Writing fast inference code for a complex spatial model with realistically‐sized datasets from scratch is time‐consuming, and if changes are made to the model, there is little guarantee that the code performs well. The key advantages of R‐INLA are the ease with which complex models can be created and modified, without the need to write complex code, and the speed at which inference can be done even for spatial problems with hundreds of thousands of observations. R‐INLA handles latent Gaussian models, where fixed effects, structured and unstructured Gaussian random effects are combined linearly in a linear predictor, and the elements of the linear predictor are observed through one or more likelihoods. The structured random effects can be both standard areal model such as the Besag and the BYM models, and geostatistical models from a subset of the Matérn Gaussian random fields. In this review, we discuss the large success of spatial modeling with R‐INLA and the types of spatial models that can be fitted, we give an overview of recent developments for areal models, and we give an overview of the stochastic partial differential equation (SPDE) approach and some of the ways it can be extended beyond the assumptions of isotropy and separability. In particular, we describe how slight changes to the SPDE approach leads to straight‐forward approaches for nonstationary spatial models and nonseparable space–time models. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory Statistical Models > Bayesian Models Data: Types and Structure > Massive Data

In several areas of application ranging from brain imaging to astrophysics and geostatistics, an important statistical problem is to find regions where the process studied exceeds a certain level. Estimating such regions so that the probability for exceeding the level in the entire set is equal to some predefined value is a difficult problem connected to the problem of multiple significance testing. In this work, a method for solving this problem, as well as the related problem of finding credible regions for contour curves, for latent Gaussian models is proposed. The method is based on using a parametric family for the excursion sets in combination with a sequential importance sampling method for estimating joint probabilities. The accuracy of the method is investigated by using simulated data and an environmental application is presented.

SummaryTo investigate the development of HLA-DR-associated autoimmune diseases, we generated transgenic (Tg) mice with HLA-DRA-IEcx and HLA-DRBI*0401-IE[3 chimeric genes. The transgene-encoded proteins consisted of antigen-binding domains from HLA-DRA and HLA-DRBI*0401 molecules and the remaining domains from the IEd-ot and IEd-[3 chains. The chimeric molecules showed the same antigen-binding specificity as HLA-DRBI*0401 molecules, and were functional in presenting antigens to T cells. The Tg mice were backcrossed to MHC class II-deficient (IAl3-,IEoe-) mice to eliminate any effect of endogenous MHC class II genes on the development of autoimmune diseases. As expected, IA~x[3 or IEot[3 molecules were not expressed in Tg mice. Moreover, cell-surface expression of endogenous IE[3 associated with HLA-DRA-IEci was not detectable in several Tg mouse lines by flow cytometric analysis. The HLA-DRA-IEo~/HLA-DRBI*0401-IE[3 molecules rescued the development ofCD4 + T cells in MHC class II-deficient mice, but T cells expressing VI35, V1311, and VI312 were specifically deleted.Tg mice were immunized with peptides, myelin basic protein (MBP) 87-106 and proteolipid protein (PLP) [175][176][177][178][179][180][181][182][183][184][185][186][187][188][189][190][191][192], that are considered to be immunodominant epitopes in HLA-DR4 individuals. PLP175-192 provoked a strong proliferative response of lymph node T cells from Tg mice, and caused inflammatory lesions in white matter of the CNS and symptoms of experimental allergic encephalomyelitis (EAE). Immunization with MBP87-106 elicited a very weak proliferative T cell response and caused mild EAE. Non-Tg mice immunized with either PLP175-192 or MBP87-106 did not develop EAE. These results demonstrated that a human MHC class II binding site alone can confer susceptibility to an experimentally induced murine autoimmune disease.