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Background Acute respiratory infections (ARI) in Cúcuta -Colombia, have a comparatively high burden of disease associated with high public health costs. However, little is known about the epidemiology of these diseases in the city and its distribution within suburban areas. This study addresses this gap by estimating and mapping the risk of ARI in Cúcuta and identifying the most relevant risk factors. Methods A spatial epidemiological analysis was designed to investigate the association of sociodemographic and environmental risk factors with the rate of ambulatory consultations of ARI in urban sections of Cúcuta, 2018. The ARI rate was calculated using a method for spatial estimation of disease rates. A Bayesian spatial model was implemented using the Integrated Nested Laplace Approximation approach and the Besag-York-Mollié specification. The risk of ARI per urban section and the hotspots of higher risk were also estimated and mapped. Results A higher risk of IRA was found in central, south, north and west areas of Cúcuta after adjusting for sociodemographic and environmental factors, and taking into consideration the spatial distribution of the city’s urban sections. An increase of one unit in the percentage of population younger than 15 years; the Index of Multidimensional Poverty and the rate of ARI in the migrant population was associated with a 1.08 (1.06—1.1); 1.04 (1.01—1.08) and 1.25 (1.22—1.27) increase of the ARI rate, respectively. Twenty-four urban sections were identified as hotspots of risk in central, south, north and west areas in Cucuta. Conclusion Sociodemographic factors and their spatial patterns are determinants of acute respiratory infections in Cúcuta. Bayesian spatial hierarchical models can be used to estimate and map the risk of these infections in suburban areas of large cities in Colombia. The methods of this study can be used globally to identify suburban areas and or specific communities at risk to support the implementation of prevention strategies and decision-making in the public and private health sectors.

A frequent challenge encountered with ecological data is how to interpret, analyze, or model data having a high proportion of zeros. Much attention has been given to zero-inflated count data, whereas models for non-negative continuous data with an abundance of 0s are much fewer. We consider zero-inflated data on the unit interval and provide modeling to capture two types of 0s in the context of a Beta regression model. We model 0s due to missing by chance through left-censoring of a latent regression and 0s due to unsuitability using an independent Bernoulli specification. We extend the model by introducing spatial random effects. We specify models hierarchically, employing latent variables, and fit them within a Bayesian framework. Our motivating dataset consists of percent cover abundance of two plant families at a collection of sites in the Cape Floristic Region of South Africa. We find that environmental features enable learning about both types of 0s as well as positive percent cover. We also show that the spatial random effects model improves predictive performance. The proposed modeling enables ecologists to extract a better understanding of an organism’s absence due to unsuitability vs. missingness by chance, as well as abundance behavior when present. Supplementary materials accompanying this paper appear online.

Randomized comparisons among several treatments give rise to an incomplete-blocks structure known as mixed treatment comparisons (MTCs). To analyze such data structures, it is crucial to assess whether the disparate evidence sources provide consistent information about the treatment contrasts. In this article we propose a general method for assessing evidence inconsistency in the framework of Bayesian hierarchical models. We begin with the distinction between basic parameters, which have prior distributions, and functional parameters, which are defined in terms of basic parameters. Based on a graphical analysis of MTC structures, evidence inconsistency is defined as a relation between a functional parameter and at least two basic parameters, supported by at least three evidence sources. The inconsistency degrees of freedom (ICDF) is the number of such inconsistencies. We represent evidence consistency as a set of linear relations between effect parameters on the log odds ratio scale, then relax these relations to allow for inconsistency by adding to the model random inconsistency factors (ICFs). The number of ICFs is determined by the ICDF. The overall consistency between evidence sources can be assessed by comparing models with and without ICFs, whereas their posterior distribution reflects the extent of inconsistency in particular evidence cycles. The methods are elucidated using two published datasets, implemented with standard Markov chain Monte Carlo software.

This paper considers penalized quantile regression model for random effects longitudinal data from a Bayesian perspective. The introduction of a large number of individual random effects can significantly inflate the variability of estimates of other covariate effects. To modify this inflation effect a hierarchical Bayesian model is introduced to shrink the individual effects toward the common population values by using the Lasso and adaptive Lasso penalties in the quantile regression check function. A Gibbs sampling algorithm is developed to simulate the parameters from the posterior distributions. The simulation studies and real data analysis indicate that the proposed methods generally perform better in comparison to the other approaches.

Background The aim of this paper was to evaluate the distribution of HIV and TB in Ethiopia during four years (2015-2018) at the district level, considering both spatial and temporal patterns. Methods Consolidated data on the count of TB case notifications and the number of patients with HIV for four years, 2015-2018, were provided by the Ethiopian Federal Ministry of Health. The data was analyzed using the Bayesian hierarchical approach, employing joint spatiotemporal modelling. The integrated nested Laplace approximation available in the R-INLA package was used to fit six models, each with different priors, for the precision parameters of the random effects variances. The best-fitting model with the best predictive capacity was selected using the Deviance Information Criterion and the negative sum of cross-validatory predictive log-likelihood. Results According to the findings of the selected model, about 53% of the variability in TB and HIV incidences in the study period was explained by the shared temporal component, disease-specific spatial effect of HIV, and space-time interaction effect. The shared temporal trend and disease-specific temporal trend of HIV risk showed a slight upward trend between 2015 and 2017, followed by a slight decrease in 2018. However, the disease-specific temporal trend of TB risk had almost constant trend with minimal variation over the study period. The distribution of the shared relative risks was similar to the distribution of disease-specific TB relative risk, whereas that of HIV had more districts as high-risk areas. Conclusions The study showed the spatial similarity in the distribution of HIV and TB case notifications in specific districts within various provinces. Moreover, the shared relative risks exhibit a temporal pattern and spatial distribution that closely resemble those of the relative risks specific to HIV illness. The existence of districts with shared relative risks implies the need for collaborative surveillance of HIV and TB, as well as integrated interventions to control the two diseases jointly.

Random effects models play an important role in model-based small area estimation. Random effects account for any lack of fit of a regression model for the population means of small areas on a set of explanatory variables. In a recent article, Datta, Hall, and Mandal showed that if the random effects can be dispensed with via a suitable test, then the model parameters and the small area means may be estimated with substantially higher accuracy. The work of Datta, Hall, and Mandal is most useful when the number of small areas, m , is moderately large. For large m , the null hypothesis of no random effects will likely be rejected. Rejection of the null hypothesis is usually caused by a few large residuals signifying a departure of the direct estimator from the synthetic regression estimator. As a flexible alternative to the Fay–Herriot random effects model and the approach in Datta, Hall, and Mandal, in this article we consider a mixture model for random effects. It is reasonably expected that small areas with population means explained adequately by covariates have little model error, and the other areas with means not adequately explained by covariates will require a random component added to the regression model. This model is a useful alternative to the usual random effects model and the data determine the extent of lack of fit of the regression model for a particular small area, and include a random effect if needed. Unlike the Datta, Hall, and Mandal approach which recommends excluding random effects from all small areas if a test of null hypothesis of no random effects is not rejected, the present model is more flexible. We used this mixture model to estimate poverty ratios for 5–17-year-old-related children for the 50 U.S. states and Washington, DC. This application is motivated by the SAIPE project of the U.S. Census Bureau. We empirically evaluated the accuracy of the direct estimates and the estimates obtained from our mixture model and the Fay–Herriot random effects model. These empirical evaluations and a simulation study, in conjunction with a lower posterior variance of the new estimates, show that the new estimates are more accurate than both the frequentist and the Bayes estimates resulting from the standard Fay–Herriot model. Supplementary materials for this article are available online.

Forest carbon stock is an important indicator reflecting a forest ecosystem’s structures and functions. Its spatial distribution is valuable for managing natural resources, protecting ecosystems and biodiversity, and further promoting sustainability, but accurately mapping the forest carbon stock distribution in a large area is a challenging task. This study selected Changting County, Fujian Province, as a case study to explore a method to map the forest carbon stock distribution using the integration of airborne Lidar, Sentinel-2, and ancillary data in 2022. The Bayesian hierarchical modeling approach was used to estimate the local forest carbon stock based on airborne Lidar data and field measurements, and then the random forest approach was used to develop a regional forest carbon stock estimation model based on the Sentinel-2 and ancillary data. The results indicated that the Lidar-based carbon stock distribution effectively provided sample plots with good spatial representativeness for modeling regional carbon stock with a coefficient of determination (R2) of 0.7 and root mean square error (RMSE) of 12.94 t/ha. The average carbon stocks were 48.55 t/ha, 55.51 t/ha, and 57.04 t/ha for Masson pine, Chinese fir, and broadleaf forests, respectively. The carbon stock in non-conservation regions was 15.2–16.1 t/ha higher than that in conservation regions. This study provides a promising method through the use of airborne Lidar data as a linkage between sample plots and Sentinel-2 data to map the regional carbon stock distribution in those subtropical regions where serious soil erosion has led to a relatively sparse forest canopy density. The results are valuable for local government to make scientific decisions for promoting ecosystem restoration due to water and soil erosion.

Turnover, or change in the composition of species over space and time, is one of the primary ways to define beta diversity. Inferring what factors impact beta diversity is not only important for understanding biodiversity processes but also for conservation planning. At present, a popular approach to understanding the drivers of compositional turnover is through generalized dissimilarity modelling (GDM). We argue that the current GDM approach suffers several limitations and provide an alternative modelling approach that remedies these issues. We propose using generative spatial random effects models implemented in a Bayesian framework. We offer hierarchical specifications to yield full regression and spatial predictive inference, both with associated full uncertainties. The approach is illustrated by examining dissimilarity in three datasets: tree survey data from Panama's Barro Colorado Island (BCI), plant occurrence data from southwest Australia and plant abundance surveys from the Greater Cape Floristic Region (GCFR) of South Africa. We select a best model using out‐of‐sample predictive performance. We find that the form of the best model differs across the three datasets, but our models provide performance ranging from comparable to significant improvement over GDMs. Within the GCFR, the spatial random effects play a more important role in the modelling than all the environmental variables. We have proposed a model that provides several improvements to the current GDM framework. This includes advantages such as a flexible spatially varying mean function, spatial random effects that capture dependence unaccounted for by explanatory variables, and spatially heterogeneous variance structure. All these features are offered in a model that can adequately handle a large incidence of total dissimilarity through ‘one‐inflation’, as would be expected from highly biodiverse areas with steep turnover gradients.

This paper illustrates the advantages of a multilevel/hierarchical approach for predictive modeling, including flexibility of model formulation, explicitly accounting for hierarchical structure in the data, and the ability to predict the outcome of new cases. As a generalization of the classical approach, the multilevel modeling approach explicitly models the hierarchical structure in the data by considering both the within- and between-group variances leading to a partial pooling of data across all levels in the hierarchy. The modeling framework provides means for incorporating variables at different spatiotemporal scales. The examples used in this paper illustrate the iterative process of model fitting and evaluation, a process that can lead to improved understanding of the system being studied.

Models of the geographic distributions of species have wide application in ecology. But the nonspatial, single-level, regression models that ecologists have often employed do not deal with problems of irregular sampling intensity or spatial dependence, and do not adequately quantify uncertainty. We show here how to build statistical models that can handle these features of spatial prediction and provide richer, more powerful inference about species niche relations, distributions, and the effects of human disturbance. We begin with a familiar generalized linear model and build in additional features, including spatial random effects and hierarchical levels. Since these models are fully specified statistical models, we show that it is possible to add complexity without sacrificing interpretability. This step-by-step approach, together with attached code that implements a simple, spatially explicit, regression model, is structured to facilitate self-teaching. All models are developed in a Bayesian framework. We assess the performance of the models by using them to predict the distributions of two plant species (Proteaceae) from South Africa's Cape Floristic Region. We demonstrate that making distribution models spatially explicit can be essential for accurately characterizing the environmental response of species, predicting their probability of occurrence, and assessing uncertainty in the model results. Adding hierarchical levels to the models has further advantages in allowing human transformation of the landscape to be taken into account, as well as additional features of the sampling process.