Latent Gaussian modeling and INLA: A review with focus on space-time applications

Bayesian hierarchical models with latent Gaussian layers have proven very flexible in capturing complex stochastic behavior and hierarchical structures in high-dimensional spatial and spatio-temporal data. Whereas simulation-based Bayesian inference through Markov Chain Monte Carlo may be hampered by slow convergence and numerical instabilities, the inferential framework of Integrated Nested Laplace Approximation (INLA) is capable to provide accurate and relatively fast analytical approximations to posterior quantities of interest. It heavily relies on the use of Gauss-Markov dependence structures to avoid the numerical bottleneck of high-dimensional nonsparse matrix computations. With a view towards space-time applications, we here review the principal theoretical concepts, model classes and inference tools within the INLA framework. Important elements to construct space-time models are certain spatial Mat\'ern-like Gauss-Markov random fields, obtained as approximate solutions to a stochastic partial differential equation. Efficient implementation of statistical inference tools for a large variety of models is available through the INLA package of the R software. To showcase the practical use of R-INLA and to illustrate its principal commands and syntax, a comprehensive simulation experiment is presented using simulated non Gaussian space-time count data with a first-order autoregressive dependence structure in time

Point process-based modeling of multiple debris flow landslides using INLA: an application to the 2009 Messina disaster

We develop a stochastic modeling approach based on spatial point processes of log-Gaussian Cox type for a collection of around 5000 landslide events provoked by a precipitation trigger in Sicily, Italy. Through the embedding into a hierarchical Bayesian estimation framework, we can use the Integrated Nested Laplace Approximation methodology to make inference and obtain the posterior estimates. Several mapping units are useful to partition a given study area in landslide prediction studies. These units hierarchically subdivide the geographic space from the highest grid-based resolution to the stronger morphodynamic-oriented slope units. Here we integrate both mapping units into a single hierarchical model, by treating the landslide triggering locations as a random point pattern. This approach diverges fundamentally from the unanimously used presence-absence structure for areal units since we focus on modeling the expected landslide count jointly within the two mapping units. Predicting this landslide intensity provides more detailed and complete information as compared to the classically used susceptibility mapping approach based on relative probabilities. To illustrate the model's versatility, we compute absolute probability maps of landslide occurrences and check its predictive power over space. While the landslide community typically produces spatial predictive models for landslides only in the sense that covariates are spatially distributed, no actual spatial dependence has been explicitly integrated so far for landslide susceptibility. Our novel approach features a spatial latent effect defined at the slope unit level, allowing us to assess the spatial influence that remains unexplained by the covariates in the model

Max-infinitely divisible models and inference for spatial extremes

For many environmental processes, recent studies have shown that the dependence strength is decreasing when quantile levels increase. This implies that the popular max-stable models are inadequate to capture the rate of joint tail decay, and to estimate joint extremal probabilities beyond observed levels. We here develop a more flexible modeling framework based on the class of max-infinitely divisible processes, which extend max-stable processes while retaining dependence properties that are natural for maxima. We propose two parametric constructions for max-infinitely divisible models, which relax the max-stability property but remain close to some popular max-stable models obtained as special cases. The first model considers maxima over a finite, random number of independent observations, while the second model generalizes the spectral representation of max-stable processes. Inference is performed using a pairwise likelihood. We illustrate the benefits of our new modeling framework on Dutch wind gust maxima calculated over different time units. Results strongly suggest that our proposed models outperform other natural models, such as the Student-t copula process and its max-stable limit, even for large block sizes

Foreign National Patients in German Prison Psychiatry

Introduction: Over the past few years, the share of foreign national prisoners in the European and American justice systems has increased at a disproportionately high rate, yet studies on mental health issues among this diverse group are rare. Recent research suggests a range of factors leading to mental health vulnerability in foreign national prisoners, including language barriers, isolation, cultural misunderstanding, and legal standing. Relevant findings of topic-related studies indicate that under-referral to mental health services due to missed or misinterpreted symptoms is a major risk for foreign national prisoners. Aims: We aimed to investigate the disparities regarding the percentage of foreign national patients who were treated in high-security hospitals compared to the psychiatric ward of prison hospitals-after adjusting for diagnosis, age, marital status, and substance abuse. We hypothesized that foreign national patients were underrepresented in compulsory, high-security mental health care. We also aimed to explore citizenship-related institutional disparities concerning diagnoses and self-harmful behavior. Method: From 2010 to 2015, data collected from high-security hospitals in the federal state of Baden-Wurttemberg and the psychiatric ward of a Berlin prison hospital was evaluated by comparing nationality, diagnosis, and self-harm using Fisher's exact test and χ²-test. The odds ratios for citizenship-related differences in diagnosis and institution of treatment were evaluated by using logistic regression. Results: Mentally ill foreign national patients were significantly less likely to be treated in high-security hospitals rather than prison hospital psychiatry (adjusted for diagnosis, age at admission, marital status, and substance abuse; adjusted OR = 0.5). Foreign nationals and Germans in prison hospital psychiatry showed no significant disparities in diagnosis; however, in high-security hospitals, foreign nationals were more likely to have been diagnosed with schizophrenia/psychotic or neurotic/stress-related disorders and were less likely to have been diagnosed with personality disorders than German patients. Additionally, foreign nationals were more likely to commit self-harm than Germans in prison hospital psychiatry, but significant citizenship-related differences could not be verified in high-security hospital patients. Conclusion: Treatment conditions of foreign national patients in prison psychiatry must be improved. To achieve this, the psychiatric assessment and (mental) health-related aspects of these patients should be further investigated

Point-process based Bayesian modeling of space-time structures of forest fire occurrences in Mediterranean France

Due to climate change and human activity, wildfires tend to become more frequent and extreme, causing economic and ecological disasters. The deployment of preventive measures and operational forecasts can be aided by stochastic modeling that helps to understand and quantify the mechanisms governing the occurrence intensity. We here use a point process framework for wildfire ignition points in the French Mediterranean basin since 1995, and we fit a spatio-temporal log-Gaussian Cox process with monthly temporal resolution in a Bayesian framework using the integrated nested Laplace approximation (INLA). Human activity is the main direct cause of wildfires and is indirectly measured through a number of appropriately defined proxies related to land-use covariates (urbanization, road network) in our model, and we further integrate covariates of climatic and environmental conditions to explain wildfire occurrences. We include spatial random effects with Matérn covariance and temporal autoregression at yearly resolution. Two major methodological challenges are tackled : first, handling and unifying multi-scale structures in data is achieved through computer-intensive preprocessing steps with GIS software and kriging techniques; second, INLA-based estimation with high-dimensional response vectors and latent models is facilitated through intra-year subsampling, taking into account the occurrence structure of wildfires