Håvard Rue

Regression models for circular variables are less developed, since the concept of building a linear predictor from linear combinations of covariates and various random effects, breaks the circular nature of the variable. In this paper, we introduce a new approach to rectify this issue, leading to well-defined regression models for circular responses when the data are concentrated. Our approach extends naturally to joint regression models where we can have several circular and non-circular responses, and allow us to handle a mix of linear covariates, circular covariates and various random effects. Our formulation aligns naturally with the integrated nested Laplace approximation (INLA), which provides fast and accurate Bayesian inference. We illustrate our approach through several simulated and real examples.

The rising threat of marine heatwaves has led to numerous predictions that coral reefs, especially those near the Equator, will be severely degraded by the end of the current century. Yet, environmental conditions near the Equator may regionally moderate coral bleaching by reducing thermal stress during marine heatwaves. We deployed a Bayesian spatio‐temporal model over Earth to examine which environmental conditions may characterize marine‐heatwave refugia for coral reefs by testing the relationship between the severity of coral bleaching and a suite of temperature, hydrodynamic, topographic, atmospheric, and biological variables. The model considered the severity of coral bleaching as the proportion of bleached hard corals during 30,266 coral‐reef surveys conducted at 8728 sites, at depths of up to 20 m, and located between 35° north and south of the Equator across 81 countries, from 2002 to 2020. Except for the eastern Pacific Ocean, the severity of coral bleaching during marine heatwaves was lower on equatorial reefs than on higher‐latitude reefs, suggesting that marine‐heatwave refugia for corals have been concentrated in the equatorial Coral Triangle region. Indeed, equatorial reefs in the Coral Triangle were, on average, exposed to the weakest marine heatwaves, potentially because they were shielded from extreme insolation by frequent cloud coverage in the Intertropical Convergence Zone. Coral bleaching may also be moderated during marine heatwaves on reefs that experience high wave energy, high current velocity, high cloud frequency, or turbidity. Coral bleaching was also less severe on reefs that historically endured frequent heatwaves than on reefs that were naïve to thermal stress. Based on modern and historical responses of coral reefs to acute thermal stress, we hypothesize that many equatorial reefs will continue to serve as marine‐heatwave refugia for corals.

Spatial Gaussian fields (SGFs) are widely employed in modeling the distributions of marine megafauna, yet they traditionally rely on assumptions of isotropy and stationarity, conditions that often prove unrealistic in complex ecological environments featuring coastlines, islands, and depth gradients acting as partial movement barriers. Existing spatial models typically treat these barriers as either fully impermeable, completely blocking species movement and dispersal, or entirely absent, which inadequately represents most real-world scenarios. To address this limitation, we introduce the Transparent Barrier Model, an extension of spatial Gaussian fields that explicitly incorporates barriers with varying levels of permeability. The model assigns spatially varying range parameters to distinct barrier regions, allowing ecological and geographical knowledge about barrier permeability to directly inform model specifications. This approach maintains computational efficiency by utilizing the integrated nested Laplace approximation (INLA) framework combined with stochastic partial differential equations (SPDEs), ensuring feasible application even in large, complex spatial domains.We demonstrate the practical utility and flexibility of the Transparent Barrier Model through its application to dugong (Dugong dugon) distribution data from the Red Sea.

In recent medical studies, the combination of longitudinal measurements with time-to-event data has increased the demand for more sophisticated models without unbiased estimates. Joint models for longitudinal and survival data have been developed to address such problems. One complex issue that may arise in the clinical trials is the presence of individuals who are statistically immune to the event of interest, those who may not experience the event even after extended follow-up periods. So far, the literature has addressed joint modeling with the presence of cured individuals mainly through mixture models for cure fraction and their extensions. In this study, we propose a joint modeling framework that accommodates the existence or absence of a cure fraction in an integrated way, using the defective Gompertz distribution. Our aim is to provide a more parsimonious alternative within an estimation process that involves a parameter vector with multiple components. Parameter estimation is performed using Bayesian inference via the efficient integrated nested Laplace approximation algorithm, by formulating the model as a latent Gaussian model. A simulation study is conducted to evaluate the frequentist properties of the proposed method under low-information prior settings. The model is further illustrated using a publicly available, yet underexplored, dataset on antiepileptic drug failure, where quality-of-life scores serve as longitudinal biomarkers. This application allows us to estimate the proportion of patients achieving seizure control under both traditional and modern antiepileptic therapies, demonstrating the model's ability to assess and compare long-term treatment effectiveness within a clinical trial context.

In this work, we present a new approach for constructing models for covariance matrices by considering the decomposition into marginal variances and a correlation matrix. The correlation structure is deduced from a user-defined graphical structure. The graphical structure makes correlation matrices interpretable and avoids the quadratic increase of parameters as a function of the dimension. We propose an automatic approach to define a prior using a natural sequence of simpler models within the Penalized Complexity framework for the unknown parameters in these models. We illustrate this approach with simulation studies of multivariate longitudinal joint modelling, where we demonstrate some properties of the method and two real data applications: a multivariate linear regression of four biomarkers and a multivariate disease mapping. Each application underscores our method’s intuitive appeal, signifying a substantial advancement toward a more cohesive and enlightening model that facilitates a meaningful interpretation of correlation matrices.

Contain code to work with latent Gaussian Markov random field (GMRF) models. Queries for the 'cgeneric' interface, specified as a way to implement new GMRF models to be fitted as model components in the 'INLA' package (). The implemented functionalities leverage the use of 'cgeneric' models and provide a way to debug the code as well to work with the prior for the model parameters and to sample from it. A Kronecker product method is also implemented to work with the four possible combinations between a 'cgeneric' and a 'rgeneric' model.

Implement some models for correlation/covariance matrices including two approaches to model correlation matrices from a graphical structure. One use latent parent variables as proposed in Sterrantino et. al. (2024) . The other uses a graph to specify conditional relations between the variables. The graphical structure makes correlation matrices interpretable and avoids the quadratic increase of parameters as a function of the dimension. In the first approach a natural sequence of simpler models along with a complexity penalization is used. The second penalizes deviations from a base model. These can be used as prior for model parameters, considering C code through the 'cgeneric' interface for the 'INLA' package (). This allows one to use these models as building blocks combined and to other latent Gaussian models in order to build complex data models.

Approximate Bayesian inference for the class of latent Gaussian models can be achieved efficiently with integrated nested Laplace approximations (INLA). Based on recent reformulations in the INLA methodology, we propose a further extension that is necessary in some cases like heavy-tailed likelihoods or binary regression with imbalanced data. This extension formulates a skewed version of the Laplace method such that some marginals are skewed and some are kept Gaussian while the dependence is maintained with the Gaussian copula from the Laplace method. Our approach is formulated to be scalable in model and data size, using a variational inferential framework enveloped in INLA. We illustrate the necessity and performance using simulated cases, as well as a case study of a rare disease where class imbalance is naturally present.