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This paper aims to extend the Besag model, a widely used Bayesian spatial model in disease mapping, to a non-stationary spatial model for irregular lattice-type data. The goal is to improve the model's ability to capture complex spatial dependence patterns and increase interpretability. The proposed model uses multiple precision parameters, accounting for different intensities of spatial dependence in different sub-regions. We derive a joint penalized complexity prior to the flexible local precision parameters to prevent overfitting and ensure contraction to the stationary model at a user-defined rate. The proposed methodology can be used as a basis for the development of various other non-stationary effects over other domains such as time. An accompanying R package fbesag equips the reader with the necessary tools for immediate use and application. We illustrate the novelty of the proposal by modeling the risk of dengue in Brazil, where the stationary spatial assumption fails and interesting risk profiles are estimated when accounting for spatial non-stationary. Additionally, we model different causes of death in Brazil, where we use the new model to investigate the spatial stationarity of these causes. [ABSTRACT FROM AUTHOR]

Gaussian processes have gained popularity in contemporary solutions for mathematical modeling problems, particularly in cases involving complex and challenging-to-model scenarios or instances with a general lack of data. Therefore, they often serve as generative models for data, for example, in classification problems. However, a common problem in the application of Gaussian processes is their computational complexity. To address this challenge, sparse methods are frequently employed, involving a reduction in the computational domain. In this study, we propose an innovative computational approach for Gaussian processes. Our method revolves around selecting a computation domain based on Chebyshev nodes, with the optimal number of nodes determined by minimizing the degree of the Chebyshev series, while ensuring meaningful coefficients derived from function values at the Chebyshev nodes with fast Fourier transform. This approach not only facilitates a reduction in computation time but also provides a means to reconstruct the original function using the functional series. We conducted experiments using two computational methods for Gaussian processes: Markov chain Monte Carlo and integrated nested Laplace approximation. The results demonstrate a significant reduction in computation time, thereby motivating further development of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This study introduces a multivariate extension to the class of stochastic volatility models, employing integrated nested Laplace approximations (INLA) for estimation. Bayesian methods for estimating stochastic volatility models through Markov Chain Monte Carlo (MCMC) can become computationally burdensome or inefficient as the dataset size and problem complexity increase. Furthermore, issues related to chain convergence can also arise. In light of these challenges, this research aims to establish a computationally efficient approach for estimating multivariate stochastic volatility models. We propose a multifactor formulation estimated using the INLA methodology, enabling an approach that leverages sparse linear algebra and parallelization techniques. To evaluate the effectiveness of our proposed model, we conduct in-sample and out-of-sample empirical analyses of stock market index return series. Furthermore, we provide a comparative analysis with models estimated using MCMC, demonstrating the computational efficiency and goodness of fit improvements achieved with our approach. [ABSTRACT FROM AUTHOR]

This study introduces a multivariate extension to the class of stochastic volatility models, employing integrated nested Laplace approximations (INLA) for estimation. Bayesian methods for estimating stochastic volatility models through Markov Chain Monte Carlo (MCMC) can become computationally burdensome or inefficient as the dataset size and problem complexity increase. Furthermore, issues related to chain convergence can also arise. In light of these challenges, this research aims to establish a computationally efficient approach for estimating multivariate stochastic volatility models. We propose a multifactor formulation estimated using the INLA methodology, enabling an approach that leverages sparse linear algebra and parallelization techniques. To evaluate the effectiveness of our proposed model, we conduct in-sample and out-of-sample empirical analyses of stock market index return series. Furthermore, we provide a comparative analysis with models estimated using MCMC, demonstrating the computational efficiency and goodness of fit improvements achieved with our approach.

Adaptive trials usually require simulations to determine values for design parameters, demonstrate error rates, and establish the sample size. We designed a Bayesian adaptive trial comparing ventilation strategies for patients with acute hypoxemic respiratory failure using simulations. The complexity of the analysis would usually require computationally expensive Markov Chain Monte Carlo methods but this barrier to simulation was overcome using the Integrated Nested Laplace Approximations (INLA) algorithm to provide fast, approximate Bayesian inference. We simulated two-arm Bayesian adaptive trials with equal randomization that stratified participants into two disease severity states. The analysis used a proportional odds model, fit using INLA. Trials were stopped based on pre-specified posterior probability thresholds for superiority or futility, separately for each state. We calculated the type I error and power across 64 scenarios that varied the probability thresholds and the initial minimum sample size before commencing adaptive analyses. Two designs that maintained a type I error below 5%, a power above 80%, and a feasible mean sample size were evaluated further to determine the optimal design. Power generally increased as the initial sample size and the futility threshold increased. The chosen design had an initial recruitment of 500 and a superiority threshold of 0.9925, and futility threshold of 0.95. It maintained high power and was likely to reach a conclusion before exceeding a feasible sample size. We designed a Bayesian adaptive trial to evaluate novel strategies for ventilation using the INLA algorithm to efficiently evaluate a wide range of designs through simulation. [ABSTRACT FROM AUTHOR]

Background: Clinical trials are increasingly using Bayesian methods for their design and analysis. Inference in Bayesian trials typically uses simulation-based approaches such as Markov Chain Monte Carlo methods. Markov Chain Monte Carlo has high computational cost and can be complex to implement. The Integrated Nested Laplace Approximations algorithm provides approximate Bayesian inference without the need for computationally complex simulations, making it more efficient than Markov Chain Monte Carlo. The practical properties of Integrated Nested Laplace Approximations compared to Markov Chain Monte Carlo have not been considered for clinical trials. Using data from a published clinical trial, we aim to investigate whether Integrated Nested Laplace Approximations is a feasible and accurate alternative to Markov Chain Monte Carlo and provide practical guidance for trialists interested in Bayesian trial design., Methods: Data from an international Bayesian multi-platform adaptive trial that compared therapeutic-dose anticoagulation with heparin to usual care in non-critically ill patients hospitalized for COVID-19 were used to fit Bayesian hierarchical generalized mixed models. Integrated Nested Laplace Approximations was compared to two Markov Chain Monte Carlo algorithms, implemented in the software JAGS and stan, using packages available in the statistical software R. Seven outcomes were analysed: organ-support free days (an ordinal outcome), five binary outcomes related to survival and length of hospital stay, and a time-to-event outcome. The posterior distributions for the treatment and sex effects and the variances for the hierarchical effects of age, site and time period were obtained. We summarized these posteriors by calculating the mean, standard deviations and the 95% equitailed credible intervals and presenting the results graphically. The computation time for each algorithm was recorded., Results: The average overlap of the 95% credible interval for the treatment and sex effects estimated using Integrated Nested Laplace Approximations was 96% and 97.6% compared with stan, respectively. The graphical posterior densities for these effects overlapped for all three algorithms. The posterior mean for the variance of the hierarchical effects of age, site and time estimated using Integrated Nested Laplace Approximations are within the 95% credible interval estimated using Markov Chain Monte Carlo but the average overlap of the credible interval is lower, 77%, 85.6% and 91.3%, respectively, for Integrated Nested Laplace Approximations compared to stan. Integrated Nested Laplace Approximations and stan were easily implemented in clear, well-established packages in R, while JAGS required the direct specification of the model. Integrated Nested Laplace Approximations was between 85 and 269 times faster than stan and 26 and 1852 times faster than JAGS., Conclusion: Integrated Nested Laplace Approximations could reduce the computational complexity of Bayesian analysis in clinical trials as it is easy to implement in R, substantially faster than Markov Chain Monte Carlo methods implemented in JAGS and stan, and provides near identical approximations to the posterior distributions for the treatment effect. Integrated Nested Laplace Approximations was less accurate when estimating the posterior distribution for the variance of hierarchical effects, particularly for the proportional odds model, and future work should determine if the Integrated Nested Laplace Approximations algorithm can be adjusted to improve this estimation., Competing Interests: Declaration of conflicting interestsThe author(s) declared the following potential conflicts of interest with respect to the research, authorship, and/or publication of this article: JSB is on the advisory board Advisory for Amgen and Janssen outside the submitted work. LAC holds a Heart and Stroke Foundation of Canada National New Investigator Award, and a Tier 2 research Chair in Thrombosis and Anticoagulation Safety from the University of Ottawa. LZK is a consultant for Cerus, Gamma Diagnostics and the University of Maryland. MDN is served as the Co-Chair of the ACTIV4a trial.

Recently, much work has been put into improving species distribution models, especially for systematic conservation planning for important ecosystems. Understanding fish spawning sites requires a thorough examination of ichthyoplankton. These examinations usually produce sparse counts contaminated by inaccurate detection, making it impossible to directly infer the abundance or occurrence from observational data, which could lead to inaccurate model predictions. A flexible modeling framework for estimating and inference about the abundance of eggs with ensemble models that include the presence/absence and abundance components is described in this study. The generalized linear model, generalized additive model, integrated nested Laplace approximations, and random forest habitat modeling approaches were compared within this framework to those currently being used for fish conservation planning at regional scales. Additionally, the distribution of suitable habitats for small yellow croaker (Larimichthys polyactis) spawning stocks were mapped based on the ensemble model. Furthermore, the promotion ability of ensemble models with different weighting methods was evaluated. The outcomes demonstrated that machine learning algorithms performed better than statistical models, and the geometric weighted ensemble model further increased prediction accuracy. However, there was no significant difference compared to the optimal individual model (p > 0.05). The predicted distributions of the four models can be divided into two groups. The central sea of Jiangsu was recognized as the most suitable area by the GAM with a fixed effect for each year and INLA models, while the GLM was similar to the RF with spatial effect (RF-LL) and demonstrated Haizhou Bay as the most suitable area. The ensemble model discovered several areas of highly suitable habitat that dominated areas in the two groups of models and revealed many finer-scale patterns in the egg distribution. According to the ensemble model, although 5.37% of the area could be suitable habitat, only 0.12% was highly suitable. It is suggested that examining small yellow croaker spawning aggregation areas would benefit from using an ensemble modeling approach to identify and prioritize conservation areas. • Using a multi-models and ensemble algorithm for sparse egg data. • Random forest model outperformed individual base models. • Identify abiotic factors contributed to spawning sites selection. • Proposed the locations and areas for priority protected areas. [ABSTRACT FROM AUTHOR]

We propose a novel analysis of power (ANOPOW) model for analyzing replicated nonstationary time series commonly encountered in experimental studies. Based on a locally stationary ANOPOW Cramér spectral representation, the proposed model can be used to compare the second-order time-varying frequency patterns among different groups of time series and to estimate group effects as functions of both time and frequency. Formulated in a Bayesian framework, independent two-dimensional second-order random walk (RW2D) priors are assumed on each of the time-varying functional effects for flexible and adaptive smoothing. A piecewise stationary approximation of the nonstationary time series is used to obtain localized estimates of time-varying spectra. Posterior distributions of the time-varying functional group effects are then obtained via integrated nested Laplace approximations (INLA) at a low computational cost. The large-sample distribution of local periodograms can be appropriately utilized to improve estimation accuracy since INLA allows modeling of data with various types of distributions. The usefulness of the proposed model is illustrated through two real data applications: analyses of seismic signals and pupil diameter time series in children with attention deficit hyperactivity disorder. Simulation studies, Supplementary Materials (Li, Yue and Bruce, 2023a), and R code (Li, Yue and Bruce, 2023b) for this article are also available.

This paper introduces the R package meta4diag for implementing Bayesian bivariate meta-analyses of diagnostic test studies. Our package meta4diag is a purpose-built front end of the R package INLA. While INLA offers full Bayesian inference for the large set of latent Gaussian models using integrated nested Laplace approximations, meta4diag extracts the features needed for bivariate meta-analysis and presents them in an intuitive way. It allows the user a straightforward model specification and offers user-specific prior distributions. Further, the newly proposed penalized complexity prior framework is supported, which builds on prior intuitions about the behaviors of the variance and correlation parameters. Accurate posterior marginal distributions for sensitivity and specificity as well as all hyperparameters, and covariates are directly obtained without Markov chain Monte Carlo sampling. Further, univariate estimates of interest, such as odds ratios, as well as the summary receiver operating characteristic (SROC) curve and other common graphics are directly available for interpretation. An interactive graphical user interface provides the user with the full functionality of the package without requiring any R programming. The package is available from the Comprehensive R Archive Network (CRAN) at https://CRAN.R-project.org/package=meta4diag/ and its usage will be illustrated using three real data examples.

Objective: To estimate trends in the prevalence of child stunting in the population of children under 5 years of age covered by public health programmes, between 2009 and 2014 in Misiones, Argentina.Methods: Using Bayesian model-based geostatistics, we evaluated 724 872 anthropometric measurements corresponding to 110 633 children. In order to identify disparities at local scale, we evaluated the hypotheses of a differential reduction of stunting according to the geographical location (at two-level spatial resolution) and to the socioeconomic level in a rural or urban environment.Results: The prevalence of stunting had fallen significantly in the province overall. Sex and age defined gender disparities at individual level, and there were regional disparities with higher prevalence values in the north and northeast regions. In these areas, stunting decreased to a greater degree during the studied period, although the spatial pattern remained smoother. Stunting increased in peripheral urban and dispersed rural areas that are socioeconomically vulnerable.Conclusions: The spatial multi-level geostatistical estimates of child undernutrition provide a precision public health tool to target public policies to those populations with the greatest need, in order to reduce health disparities. [ABSTRACT FROM AUTHOR]

Summary: Crimes against women in India have been continuously increasing lately as reported by the National Crime Records Bureau. Gender‐based violence has become a serious issue to such an extent that it has been catalogued as a high impact health problem by the World Health Organization. However, there is a lack of spatiotemporal analyses to reveal a complete picture of the geographical and temporal patterns of crimes against women. We focus on analysing how the geographical pattern of 'dowry deaths' changes over time in the districts of Uttar Pradesh during the period 2001–2014. The study of the geographical distribution of dowry death incidence and its evolution over time aims to identify specific regions that exhibit high risks and to hypothesize on potential risk factors. We also look into different spatial priors and their effects on final risk estimates. Various priors for the hyperparameters are also reviewed. The risk estimates seem to be robust in terms of the spatial prior and hyperprior choices and final results highlight several districts with extreme risks of dowry death incidence. Statistically significant associations are also found between dowry deaths, sex ratio and some forms of overall crime. [ABSTRACT FROM AUTHOR]

Cardiovascular diseases (CVDs) are the leading cause of death globally and the number one cause of death globally. Over 75% of CVD deaths take place in low- and middle-income countries. Hence, comprehensive information about the spatio-temporal distribution of mortality due to cardio vascular disease is of interest. We fitted different spatio-temporal models within Bayesian hierarchical framework allowing different space-time interaction for mortality mapping with integrated nested Laplace approximations to analyze mortality data extracted from the health and demographic surveillance system in Kersa District in Hararege, Oromia Region, Ethiopia. The result indicates that non-parametric time trends models perform better than linear models. Among proposed models, one with non-parametric trend, type II interaction and second order random walk but without unstructured time effect was found to perform best according to our experience and. simulation study. An application based on real data revealed that, mortality due to CVD increased during the study period, while administrative regions in northern and south-eastern part of the study area showed a significantly elevated risk. The study highlighted distinct spatiotemporal clusters of mortality due to CVD within the study area. The study is a preliminary assessment step in prioritizing areas for further and more comprehensive research raising questions to be addressed by detailed investigation. Underlying contributing factors need to be identified and accurately quantified.

Disease risk maps for areal unit data are often estimated from Poisson mixed models with local spatial smoothing, for example by incorporating random effects with a conditional autoregressive prior distribution. However, one of the limitations is that local discontinuities in the spatial pattern are not usually modelled, leading to over-smoothing of the risk maps and a masking of clusters of hot/coldspot areas. In this paper, we propose a novel two-stage approach to estimate and map disease risk in the presence of such local discontinuities and clusters. We propose approaches in both spatial and spatio-temporal domains, where for the latter the clusters can either be fixed or allowed to vary over time. In the first stage, we apply an agglomerative hierarchical clustering algorithm to training data to provide sets of potential clusters, and in the second stage, a two-level spatial or spatio-temporal model is applied to each potential cluster configuration. The superiority of the proposed approach with regard to a previous proposal is shown by simulation, and the methodology is applied to two important public health problems in Spain, namely stomach cancer mortality across Spain and brain cancer incidence in the Navarre and Basque Country regions of Spain. [ABSTRACT FROM AUTHOR]

Functional analysis of variance (ANOVA) modeling has been proved particularly useful to investigate the dynamic changes of functional data according to certain categorical factors and their interactions. The current existing methods often encounter difficulties when the functional data are high-dimensional, non- Gaussian, and/or exhibit certain shape characteristics that vary with spatial locations. In this paper, we investigate the functional two-way ANOVA models from a novel Bayesian perspective. A class of highly exible Gaussian Markov random fields (GMRF) are taken as priors on the functions in the model, which allows us to model various types of functional effects, such as (discrete or continuous) temporal effects and (point-level or areal) spatial effects. The resulting posterior distributions are obtained by an efficient computational tool based on integrated nested Laplace approximations (INLA) Rue, Martino and Chopin (2009). We then employ the excursion method introduced by Bolin and Lindgren (2015) to build simultaneous credible intervals of functional effects and test their significance from a Bayesian point of view. A simulation study and multiple data examples are presented to demonstrate the merits of our method. [ABSTRACT FROM AUTHOR]

In this paper age-space-time models based on one and two-dimensional P-splines with B-spline bases are proposed for smoothing mortality rates, where both fixed relative scale and scale invariant two-dimensional penalties are examined. Model fitting and inference are carried out using integrated nested Laplace approximations, a recent Bayesian technique that speeds up computations compared to McMC methods. The models will be illustrated with Spanish breast cancer mortality data during the period 1985-2010, where a general decline in breast cancer mortality has been observed in Spanish provinces in the last decades. The results reveal that mortality rates for the oldest age groups do not decrease in all provinces. [ABSTRACT FROM AUTHOR]

Abstract Trip purpose inference is critical in transportation demand management (TDM) as well as traffic congestion alleviation. However, destination choice can be affected by a variety of factors, many of which are difficult to determine (e.g. socio-demographics). Besides, the spatio-temporal variation and correlation inherent in travel patterns further intensify the difficulty of understanding destination choice behavior. To this end, this research proposes a Bayesian hierarchical approach for modeling the destination choice behavior through time and space. The proposed method can take into account both the unavailable factors and spatio-temporal correlations by introducing random fields. Moreover, the implementation of the Integrated Nested Laplace Approximations (INLA) combined with the Stochastic Partial Differential Equation (SPDE) makes it computationally feasible to model large-scale spatio-temporal correlation structures. The model is further applied to two-week data from more than 8000 taxis in Harbin. The empirical results indicate that the proposed approach is capable to capture spatio-temporal variability in destination distribution, and the inclusion of spatial and temporal random effects is of great help to improve the model performance. The case study also examines how the land-use types influence the destination choice. It is believed that the modeling method and the exploratory spatial–temporal analysis of destination distribution in this study can enriches the methodologies for travel demand modeling as well as decision support for transport policy development. Highlights • A Bayesian hierarchical model is used to study the destination choice behavior through time and space. • INLA and SPDE are combined to model large-scale spatio-temporal correlation structures. • Two-week data from more than 8000 taxis in Harbin are used in the model validation. • The results show the model is capable to capture spatio-temporal variability of destination. • The case study also examines effect of the land-use types to destination choice. [ABSTRACT FROM AUTHOR]

Summary: Although there is a literature on the distribution of food stores across geographic and social space, much of this research uses cross‐sectional data. Analyses attempting to understand whether the availability of stores across neighbourhoods is associated with diet and/or health outcomes are limited by a lack of understanding of factors that shape the emergence of new stores and the closure of others. We used quarterly data on supermarket and convenience store locations spanning seven years (2006–2012) and tract level census data in four US cities: Birmingham, Alabama; Chicago, Illinois; Minneapolis, Minnesota; San Francisco, California. A spatial discrete time survival model was used to identify factors that are associated with an earlier and/or later closure time of a store. Sales volume was typically the strongest indicator of store survival. We identified heterogeneity in the association between tract level poverty and racial composition with respect to store survival. Stores in high poverty, non‐white tracts were often at a disadvantage in terms of survival length. The observed patterns of store survival varied by some of the same neighbourhood sociodemographic factors as associated with lifestyle and health outcomes, which could lead to confusion in interpretation in studies of the estimated effects of introduction of food stores into neighbourhoods on health. [ABSTRACT FROM AUTHOR]

Air pollution is a major risk factor for global health, with 3 million deaths annually being attributed to fine particulate matter ambient pollution (PM2.5). The primary source of information for estimating population exposures to air pollution has been measurements from ground monitoring networks but, although coverage is increasing, regions remain in which monitoring is limited. The data integration model for air quality supplements ground monitoring data with information from other sources, such as satellite retrievals of aerosol optical depth and chemical transport models. Set within a Bayesian hierarchical modelling framework, the model allows spatially varying relationships between ground measurements and other factors that estimate air quality. The model is used to estimate exposures, together with associated measures of uncertainty, on a high resolution grid covering the entire world from which it is estimated that 92% of the world's population reside in areas exceeding the World Health Organization's air quality guidelines. [ABSTRACT FROM AUTHOR]

Background: Hantavirus disease in humans is rare but frequently lethal in the Neotropics. Several abundant and widely distributed Sigmodontinae rodents are the primary hosts of Orthohantavirus and, in combination with other factors, these rodents can shape hantavirus disease. Here, we assessed the influence of host diversity, climate, social vulnerability and land use change on the risk of hantavirus disease in Brazil over 24 years. Methods: Landscape variables (native forest, forestry, sugarcane, maize and pasture), climate (temperature and precipitation), and host biodiversity (derived through niche models) were used in spatiotemporal models, using the 5570 Brazilian municipalities as units of analysis. Results: Amounts of native forest and sugarcane, combined with temperature, were the most important factors influencing the increase of disease risk. Population at risk (rural workers) and rodent host diversity also had a positive effect on disease risk. Conclusions: Land use change—especially the conversion of native areas to sugarcane fields—can have a significant impact on hantavirus disease risk, likely by promoting the interaction between the people and the infected rodents. Our results demonstrate the importance of understanding the interactions between landscape change, rodent diversity, and hantavirus disease incidence, and suggest that land use policy should consider disease risk. Meanwhile, our risk map can be used to help allocate preventive measures to avoid disease.

Understanding the spatial distribution and identifying environmental variables that drive endangered fish species abundance are key factors to implement sustainable fishery management strategies. In the present study we proposed hierarchical Bayesian spatial models to quantify and map sensitive habitats for juveniles, adults and overall abundance of the vulnerable lane snapper ( Lutjanus synagris ) present in the northeastern Brazil. Data were collected by fishery-unbiased gillnet surveys, and fitted through the Integrated Nested Laplace Approximations (INLA) and the Stochastic Partial Differential Equations (SPDE) tools, both implemented in the R environment by the R-INLA library ( http://www.r-inla.org ). Our results confirmed that the abundance of juveniles and adults of L. synagris are spatially correlated, have patchy distributions along the Rio Grande do Norte coast, and are mainly affected by environmental predictors such as distance to coast, chlorophyll- a concentration, bathymetry and sea surface temperature. By means of our results we intended to consolidate a recently introduced Bayesian geostatistical model into fisheries science, highlighting its potential for establishing more reliable measures for the conservation and management of vulnerable fish species even when data are sparse. [ABSTRACT FROM AUTHOR]

We introduce new estimation methods for a subclass of the Gaussian scale mixture models for wavelet trees by Wainwright, Simoncelli and Willsky that rely on modern results for composite likelihoods and approximate Bayesian inference. Our methodology is illustrated for denoising and edge detection problems in two-dimensional images. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Functional traits, rather than taxonomic identity, determine the fitness of individuals in their environment: traits of marine organisms are therefore expected to vary across the global ocean as a function of the environment. Here, we quantify such spatial and seasonal variations based on extensive empirical data and present the first global biogeography of key traits (body size, feeding mode, relative offspring size and myelination) for pelagic copepods, the major group of marine zooplankton. We identify strong patterns with latitude, season and between ocean basins that are partially ( c. 50%) explained by key environmental drivers. Body size, for example decreases with temperature, confirming the temperature-size rule, but surprisingly also with productivity, possibly driven by food-chain length and size-selective predation. Patterns unrelated to environmental predictors may originate from phylogenetic clustering. Our maps can be used as a test-bed for trait-based mechanistic models and to inspire next-generation biogeochemical models. [ABSTRACT FROM AUTHOR]

Obtaining reliable estimates about health outcomes for areas or domains where only few to no samples are available is the goal of small area estimation (SAE). Often, we rely on health surveys to obtain information about health outcomes. Such surveys are often characterised by a complex design, stratification, and unequal sampling weights as common features. Hierarchical Bayesian models are well recognised in SAE as a spatial smoothing method, but often ignore the sampling weights that reflect the complex sampling design. In this paper, we focus on data obtained from a health survey where the sampling weights of the sampled individuals are the only information available about the design. We develop a predictive model-based approach to estimate the prevalence of a binary outcome for both the sampled and non-sampled individuals, using hierarchical Bayesian models that take into account the sampling weights. A simulation study is carried out to compare the performance of our proposed method with other established methods. The results indicate that our proposed method achieves great reductions in mean squared error when compared with standard approaches. It performs equally well or better when compared with more elaborate methods when there is a relationship between the responses and the sampling weights. The proposed method is applied to estimate asthma prevalence across districts. [ABSTRACT FROM AUTHOR]

The West Nile virus (WNv) continues to be a public health concern in North America. Dry weather appears to increase human WNv infection risks, but it is uncertain whether dry weather conditions exert similar effects on the corresponding equine WNv infection. This study assessed the effects of precipitation of the previous year and land cover diversity on the equine WNv risk of Mississippi, USA, at the county level in the year 2002 using Bayesian hierarchical models. The risk estimated for 2002 was found to be inversely related to annual precipitation of the preceding year. Equine WNv risks were lower with greater land cover diversity probably due to the diluting effects of biodiversity. Correlation between the equine and human WNv risks was positive but relatively low. Dry weather conditions of the previous year might reduce mosquito competitors and predators and subsequently increase mosquito abundances and equine WNv risks in agricultural areas with low biodiversity.

Spatial aggregation with respect to a population distribution involves estimating aggregate population quantities based on observations from individuals. In this context, a geostatistical workflow must account for three major sources of aggregation error : aggregation weights, fine scale variation, and finite population variation. However, these sources of aggregation error are commonly ignored, and the population instead treated as a fixed population density surface. We improve common practice by introducing a sampling frame model allowing aggregation models to account for aggregation error simply and transparently. This preserves aggregate point estimates while increasing their uncertainties. We compare the proposed and the traditional approach using two simulation studies mimicking neonatal mortality rate (NMR) data from the 2014 Kenya Demographic and Health Survey. In the traditional approach, undercoverage/overcoverage of interval estimates depends arbitrarily on the aggregation grid resolution, while the new approach is resolution robust. Differences between the aggregation approaches increase as an area's population decreases, and are particularly large at the second administrative level and finer, but also at the first administrative level for some population quantities. These findings are consistent with those of an application to the true NMR data. We demonstrate in a sensitivity analysis that burden estimates and their uncertainties are not robust to changes in population density and census information, while prevalence estimates and uncertainties seem stable. [ABSTRACT FROM AUTHOR]

Clustered observations such as longitudinal data are often analysed with generalized linear mixed models (GLMM). Approximate Bayesian inference for GLMMs with normally distributed random effects can be done using integrated nested Laplace approximations (INLA), which is in general known to yield accurate results. However, INLA is known to be less accurate for GLMMs with binary response. For longitudinal binary response data it is common that patients do not change their health state during the study period. In this case the grouping covariate perfectly predicts a subset of the response, which implies a monotone likelihood with diverging maximum likelihood (ML) estimates for cluster-specific parameters. This is known as quasi-complete separation. In this paper we demonstrate, based on longitudinal data from a randomized clinical trial and two simulations, that the accuracy of INLA decreases with increasing degree of cluster-specific quasi-complete separation. Comparing parameter estimates by INLA, Markov chain Monte Carlo sampling and ML shows that INLA increasingly deviates from the other methods in such a scenario. [ABSTRACT FROM PUBLISHER]

In recent years, disease mapping studies have become a routine application within geographical epidemiology and are typically analysed within a Bayesian hierarchical model formulation. A variety of model formulations for the latent level have been proposed but all come with inherent issues. In the classical BYM (Besag, York and Mollié) model, the spatially structured component cannot be seen independently from the unstructured component. This makes prior definitions for the hyperparameters of the two random effects challenging. There are alternative model formulations that address this confounding; however, the issue on how to choose interpretable hyperpriors is still unsolved. Here, we discuss a recently proposed parameterisation of the BYM model that leads to improved parameter control as the hyperparameters can be seen independently from each other. Furthermore, the need for a scaled spatial component is addressed, which facilitates assignment of interpretable hyperpriors and make these transferable between spatial applications with different graph structures. The hyperparameters themselves are used to define flexible extensions of simple base models. Consequently, penalised complexity priors for these parameters can be derived based on the information-theoretic distance from the flexible model to the base model, giving priors with clear interpretation. We provide implementation details for the new model formulation which preserve sparsity properties, and we investigate systematically the model performance and compare it to existing parameterisations. Through a simulation study, we show that the new model performs well, both showing good learning abilities and good shrinkage behaviour. In terms of model choice criteria, the proposed model performs at least equally well as existing parameterisations, but only the new formulation offers parameters that are interpretable and hyperpriors that have a clear meaning. [ABSTRACT FROM AUTHOR]

This work focuses on extending some classical spatio-temporal models in disease mapping. The objective is to present a family of flexible models to analyze real data naturally organized in two different levels of spatial aggregation like municipalities within health areas or provinces, or counties within states. Model fitting and inference will be carried out using integrated nested Laplace approximations. The performance of the new models compared to models including a single spatial random effect is assessed by simulation. Results show good behavior of the proposed two-level spatially structured models in terms of several criteria. Brain cancer mortality data in the municipalities of two regions in Spain will be analyzed using the new model proposals. It will be shown that a model with two-level spatial random effects overcomes the usual single-level models. [ABSTRACT FROM AUTHOR]

Analyzing the collected evidence of a systematic review in form of a network meta-analysis (NMA) enjoys increasing popularity and provides a valuable instrument for decision making. Bayesian inference of NMA models is often propagated, especially if correlated random effects for multiarm trials are included. The standard choice for Bayesian inference is Markov chain Monte Carlo (MCMC) sampling, which is computationally intensive. An alternative to MCMC sampling is the recently suggested approximate Bayesian method of integrated nested Laplace approximations (INLA) that dramatically saves computation time without any substantial loss in accuracy. We show how INLA apply to NMA models for summary level as well as trial-arm level data. Specifically, we outline the modeling of multiarm trials and inference for functional contrasts with INLA. We demonstrate how INLA facilitate the assessment of network inconsistency with node-splitting. Three applications illustrate the use of INLA for a NMA. [ABSTRACT FROM AUTHOR]

In this paper we analyze the spatio-temporal dynamics of brain tumors. These objects are originally processed from computer tomography images, and can be depicted as a collection of image pixels with varying degrees of color intensity levels. We consider spatio-temporal stochastic processes within a Bayesian framework to model spatial heterogeneity, temporal dependence and spatio-temporal interactions amongst the pixels, providing a general modeling framework for such dynamics. We aim at predicting cancer growth in space and time. We analyze real data on brain tumor based on a set of images taken in several time lags. [ABSTRACT FROM AUTHOR]

Acoustic telemetry is an active field of research integral to the study of marine life. The latest generation of acoustic tags is making available new types of data. As part of the Ocean Tracking Network (OTN) ( www.oceantrackingnework.org ) acoustic tags known as VEMCO Mobile Transceivers (VMTs) ( www.vemco.com ) are being deployed on Sable Island grey seals ( Halichoerus grypus ) in order to record instances of proximity to each other (as well as any other acoustically tagged animals). The seals essentially become bioprobes yielding data exhibiting both spatial and temporal variation. Fortunately, recent developments in the field of spatial statistics have greatly facilitated the fitting of complex spatial and spatio-temporal models. Here we specifically propose a hierarchical spatio-temporal model framework and fit it to these data using both Stochastic Partial Differential Equations (SPDE) and Integrated Nested Laplace Approximations (INLA) through R-INLA ( www.r-inla.org ). In so doing we demonstrate the effectiveness and advantages of these techniques. These methods readily extend to spatially explicit data collected by any sort of mobile receiving platform (e.g. wave gliders, remotely operated underwater vehicles). [ABSTRACT FROM AUTHOR]

Conditional auto-regressive models are commonly used to capture spatial cor relation in areal unit data, as part of a hierarchical Bayesian model. The spatial correlation structure that is induced by these models is determined by geographical adjacency, but this is too simplistic for some real data sets, which can visually exhibit subregions of strong correlation as well as locations at which the response exhibits a step change. An example of this, and the motivation for the paper, is the spatial pattern in respiratory disease risk in the 271 intermed iate geographies in the Greater Glasgow and Clyde Health Board in 2005. The methodology proposed is an extension to the class of conditional auto-regressive priors, which allow them to capture such localized spatial correlation and to identify step changes. The approach takes the form of an iterative algorithm, which sequentially updates the spatial correlation structure that is assumed by the model in addition to estimating the remaining parameters. The efficacy of the approach is assessed by simulation, before being applied to the motivating Greater Glasgow application. [ABSTRACT FROM AUTHOR]

Abstract: This paper introduces dynamic time series modeling in a Bayesian framework to uncover temporal patterns in highway crashes in Connecticut. Existing state sources provide data describing the time for each crash and demographic attributes of persons involved over the time period from January 1995 to December 2009 as well as the traffic volumes and the characteristics of the roads on which these crashes occurred. Induced exposure techniques are used to estimate the exposure for senior and non-senior drivers by road access type (limited access and surface roads) and area type (urban or rural). We show that these dynamic models fit the data better than the usual GLM framework while also permitting discovery of temporal trends in the estimation of parameters, and that computational difficulties arising from Markov Chain Monte Carlo (MCMC) techniques can be handled by the innovative Integrated Nested Laplace Approximations (INLA). Using these techniques we find that while overall safety is increasing over time, the level of safety for senior drivers has remained more stagnant than for non-senior drivers, particularly on rural limited access roads. The greatest opportunity for improvement of safety for senior drivers is on rural surface roads. [Copyright &y& Elsevier]

Spatiotemporal disease mapping models have been used extensively to describe the pattern of surveillance data. They are usually formulated in a hierarchical Bayesian framework and posterior marginals are not available in closed form. Hence, the standard method for parameter estimation is Markov chain Monte Carlo algorithms. A new method for approximate Bayesian inference in latent Gaussian models using integrated nested Laplace approximations has recently been proposed as an alternative. This approach promises very precise results in short computational time. The aim of the paper is to show how integrated nested Laplace approximations can be used as an inferential tool for a variety of spatiotemporal models for the analysis of reported cases of bovine viral diarrhoea in cattle from Switzerland. Conclusions concerning the problem of under-reporting in the data are drawn via a multilevel modelling strategy. Furthermore, a comparison with Markov chain Monte Carlo methods with regard to the accuracy of the parameter estimates and the usability of both approaches in practice is conducted. Approaches to model choice using integrated nested Laplace approximations are also presented. [ABSTRACT FROM AUTHOR]

Generalized linear mixed models (GLMMs) continue to grow in popularity due to their ability to directly acknowledge multiple levels of dependency and model different data types. For small sample sizes especially, likelihood-based inference can be unreliable with variance components being particularly difficult to estimate. A Bayesian approach is appealing but has been hampered by the lack of a fast implementation, and the difficulty in specifying prior distributions with variance components again being particularly problematic. Here, we briefly review previous approaches to computation in Bayesian implementations of GLMMs and illustrate in detail, the use of integrated nested Laplace approximations in this context. We consider a number of examples, carefully specifying prior distributions on meaningful quantities in each case. The examples cover a wide range of data types including those requiring smoothing over time and a relatively complicated spline model for which we examine our prior specification in terms of the implied degrees of freedom. We conclude that Bayesian inference is now practically feasible for GLMMs and provides an attractive alternative to likelihood-based approaches such as penalized quasi-likelihood. As with likelihood-based approaches, great care is required in the analysis of clustered binary data since approximation strategies may be less accurate for such data. [ABSTRACT FROM PUBLISHER]

It is widely accepted that spatial dependencies have to be acknowledged appropriately in data that are spatially aligned. However, most spatial models still assume that the dependence structure does not vary over space, i.e., it is stationary. While assuming stationarity considerably facilitates estimation, it is often too restrictive when describing atmospheric phenomena such as precipitation. Nonetheless, the applicability of non-stationary models is often hindered, as their use reveals to be cumbersome and improvements over stationary models can be hard to identify. The stochastic partial differential equation (SPDE) approach to spatial modelling allows for flexible specifications of non-stationary models. In particular, given the German orographic diversity, it makes sense to investigate potential non-stationarity in precipitation patterns. Taking such potential non-stationarities into account may, in particular, leads to improved smoothing of the observed precipitation pattern taken on a finite set of measurement stations, and therefore to improved inputs to hydrological models. We suggest an SPDE-based model where the mean and dependence structure are allowed to vary with elevation, as well as a more flexible non-parametric alternative based on multivariate B-Splines. As factors such as wind may cause higher dependence in a given direction, we include anisotropy in the model. Results show that, according to the widely applicable Bayesian information criterion, a non-stationary model provides a better fit to the data. Taking German monthly precipitation as a motivation, we set up a simulation study to explore the ability of the elevation and spline-based models to correctly identify non-stationarity. [ABSTRACT FROM AUTHOR]

• An introduced oomycete pathogen is causing serious mortality of juniper in the UK. • We used spatially explicit statistical models to explore a range of disease drivers. • The area of symptomatic juniper increased in waterlogged soils. • Analysis of field scale data identified populations at highest infection risk. • Juniper stands growing in dry soil conditions should be prioritised for conservation. The oomycete plant pathogen, Phytophthora austrocedri , is an aggressive killer of cypress trees causing severe mortality of Chilean cedar (Austrocedrus chilensis) in Argentina since the 1940 s and now of common juniper (Juniperus communis s.l.) in the UK. Rapid mortality of key UK juniper populations was first observed in the early 2000 s. The causal agent of mortality was confirmed as P. austrocedri in 2012 and the pathogen has now been widely detected - but is not ubiquitous - in juniper populations across Scotland and England. Although juniper has a broad distribution across the northern hemisphere, the UK incidence of P. austrocedri remains the only confirmed infection of juniper populations globally. Juniper is an important species for biodiversity, so it is imperative to understand the abiotic and biotic drivers of emergent P. austrocedri infection to inform detection, containment and conservation strategies to manage juniper populations across the full extent of its range. As management of UK juniper populations is primarily conducted at a local level, we investigated field scale drivers of disease – in three, geographically separate populations with different infection histories. Variation in the proportion of juniper showing symptoms - discoloured or dead foliage – was measured using stratified sampling across along key environmental gradients within each 100-hectare population. Potential predictors of infection included altitude, slope, distance to nearest watercourse, soil moisture (mean percentage volumetric water content), area of red deer browsing damage and area of commonly associated vascular plant species. We assessed support in the data for alternative models explaining the spatial distribution of P. austrocedri symptoms using full subset covariate selection and Deviance Information Criteria (DIC). Despite differences in environmental gradients and infection histories between populations, area of juniper symptomatic for P. austrocedri increased with waterlogging, increasing with soil moisture in sites where soils had higher peat or clay contents, and decreasing with proximity to watercourses where sites had shallower, sandier soils. Furthermore, we identified common taxa in the associated plant community that correlated with increased area of symptoms and could be used by land managers as indicators to identify microsites at high risk of infection, enabling site-specific tailoring of disease management strategies. Such strategies could include prioritising detection inspections in microsites with high water tables and high grazing pressure (guided by indicator taxa), limiting soil disturbance in wet microsites and creating sites for natural regeneration in drier microsites, to minimise pathogen spread and maximise the resilience of existing juniper populations. [ABSTRACT FROM AUTHOR]

Background: Hantavirus disease in humans is rare but frequently lethal in the Neotropics. Several abundant and widely distributed Sigmodontinae rodents are the primary hosts of Orthohantavirus and, in combination with other factors, these rodents can shape hantavirus disease. Here, we assessed the influence of host diversity, climate, social vulnerability and land use change on the risk of hantavirus disease in Brazil over 24 years. Methods: Landscape variables (native forest, forestry, sugarcane, maize and pasture), climate (temperature and precipitation), and host biodiversity (derived through niche models) were used in spatiotemporal models, using the 5570 Brazilian municipalities as units of analysis. Results: Amounts of native forest and sugarcane, combined with temperature, were the most important factors influencing the increase of disease risk. Population at risk (rural workers) and rodent host diversity also had a positive effect on disease risk. Conclusions: Land use change—especially the conversion of native areas to sugarcane fields—can have a significant impact on hantavirus disease risk, likely by promoting the interaction between the people and the infected rodents. Our results demonstrate the importance of understanding the interactions between landscape change, rodent diversity, and hantavirus disease incidence, and suggest that land use policy should consider disease risk. Meanwhile, our risk map can be used to help allocate preventive measures to avoid disease. [ABSTRACT FROM AUTHOR]