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BACKGROUND: Statistical and machine learning models are commonly used to estimate spatial and temporal variability in exposure to environmental stressors, supporting epidemiological studies. We aimed to compare the performances, strengths and limitations of six different algorithms in the retrospective spatiotemporal modeling of daily birch and grass pollen concentrations at a spatial resolution of 1 km across Switzerland. METHODS: Daily birch and grass pollen concentrations were available from 14 measurement sites in Switzerland for 2000-2019. To develop the spatiotemporal models, we considered spatial-temporal, spatial and temporal predictors including meteorological factors, land-use, elevation, species distribution and Normalized Difference Vegetation Index (NDVI). We used six statistical and machine learning algorithms: LASSO, Ridge, Elastic net, Random forest, XGBoost and ANNs. We optimized model structures through feature selection and grid search techniques to obtain the best predictive performance. We used train-test split and cross-validation to avoid overfitting and overoptimistic performance indicators. We then combined these six models through multiple linear regression to develop an ensemble hybrid model. RESULTS: The 5th-95th percentiles of birch and grass pollen concentrations were 0-151 and 0-105 grains/m3, respectively. The hybrid ensemble model achieved the best RMSE on the test dataset for both birch and grass pollen with 94.4 and 19.7 grains/m3, respectively. Nonlinear models (Random forest, XGBoost and ANNs) achieved lower test RMSE's than linear models (LASSO, Ridge, Elastic net) for both pollen types, with RMSE's ranging from 105.9 to 140.5 grains/m3 for birch and from 20 to 25.4 grains/m3 for grass pollen. The Random forest algorithm yielded the best spatial and temporal performance among the six evaluated modelling methods. The ensemble hybrid model outperformed the six linear and nonlinear algorithms. Country-wide pollen concentration, land use, weather, and NDVI were important predictors. CONCLUSION: Nonlinear algorithms outperformed linear models and accurately explained complex, nonlinear relationships between environmental factors and measured concentrations.

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Bayesian inference in modelling infectious diseases using Bayesian inference using Gibbs Sampling (BUGS) is notable in the last two decades in parallel with the advancements in computing and model development. The ability of BUGS to easily implement the Markov chain Monte Carlo (MCMC) method brought Bayesian analysis to the mainstream of infectious disease modelling. However, with the existing software that runs MCMC to make Bayesian inferences, it is challenging, especially in terms of computational complexity, when infectious disease models become more complex with spatial and temporal components, in addition to the increasing number of parameters and large datasets. This study investigates two alternative subscripting strategies for creating models in Just Another Gibbs Sampler (JAGS) environment and their performance in terms of run times. Our results are useful for practitioners to ensure the efficiency and timely implementation of Bayesian spatiotemporal infectious disease modelling.

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Estimation and prediction of subnational mortality rates for small areas are essential planning tools for studying health inequalities. Standard methods do not perform well when data are noisy, a typical behavior of subnational datasets. Thus, reliable estimates are difficult to obtain. I present a Bayesian hierarchical model framework for prediction of mortality rates at a small or subnational level. By combining ideas from demography and epidemiology, the classical mortality modeling framework is extended to include an additional spatial component capturing regional heterogeneity. Information is pooled across neighboring regions and smoothed over time and age. To make predictions more robust and address the issue of model selection, a Bayesian version of stacking is considered using leave-future-out validation. I apply this method to forecast mortality rates for 96 regions in Bavaria, Germany, disaggregated by age and sex. Uncertainty surrounding the forecasts is provided in terms of prediction intervals. Using posterior predictive checks, I show that the models capture the essential features and are suitable to forecast the data at hand. On held-out data, my predictions outperform those of standard models lacking a regional component.

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OBJECTIVES: Socioeconomic inequalities have played a significant role in the unequal coverage of the COVID-19 vaccine. The objectives of this study were to (1) assess the socioeconomic inequalities in COVID-19 vaccination coverage in Catalonia, Spain; (2) analyse the spatial variation over time of these inequalities; and (3) assess variations in time and space in the effect of vaccination on inequalities in COVID-19 outcomes. STUDY DESIGN: A mixed longitudinal ecological study design was used. METHODS: Catalonia is divided in to 373 Basic Health Areas. Weekly data from these Basic Health Areas were obtained from the last week of December 2020 until the first week of March of 2022. A joint spatio-temporal model was used with the dependent variables of vaccination and COVID-19 outcomes, which were estimated using a Bayesian approach. The study controlled for observed confounders, unobserved heterogeneity, and spatial and temporal dependencies. The study allowed the effect of the explanatory variables on the dependent variables to vary in space and in time. RESULTS: Areas with lower socioeconomic level were those with the lowest vaccination rates and the highest risk of COVID-19 outcomes. In general, individuals in areas that were located in the upper two quartiles of average net income per person and in the lower two quartiles of unemployment rate (i.e., the least economically disadvantaged) had a higher propensity to be vaccinated than those in the most economically disadvantaged areas. In the same sense, the greater the percentage of the population aged ≥65 years, the higher the propensity to be vaccinated, while areas located in the two upper quartiles of population density and areas with a high percentage of poor housing had a lower propensity to be vaccinated. Higher vaccination rates reduced the risk of COVID-19 outcomes, while COVID-19 outcomes did not influence the propensity to be vaccinated. The effects of the explanatory variables were not the same in all areas or between the different waves of the pandemic, and clusters of excess risk of low vaccination in the most disadvantaged areas were detected. CONCLUSIONS: COVID-19 vaccination inequalities in the most disadvantaged areas could be a result of structural barriers, such as the lack of access to information about the vaccination process, and/or logistical challenges, such as the lack of transportation, limited Internet access or difficulty in scheduling appointments. Public health strategies should be developed to mitigate these barriers and reduce vaccination inequalities.

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BACKGROUND: Opioid-related overdose mortality has remained at crisis levels across the United States, increasing 5-fold and worsened during the COVID-19 pandemic. The ability to provide forecasts of opioid-related mortality at granular geographical and temporal scales may help guide preemptive public health responses. Current forecasting models focus on prediction on a large geographical scale, such as states or counties, lacking the spatial granularity that local public health officials desire to guide policy decisions and resource allocation. OBJECTIVE: The overarching objective of our study was to develop Bayesian spatiotemporal dynamic models to predict opioid-related mortality counts and rates at temporally and geographically granular scales (ie, ZIP Code Tabulation Areas [ZCTAs]) for Massachusetts. METHODS: We obtained decedent data from the Massachusetts Registry of Vital Records and Statistics for 2005 through 2019. We developed Bayesian spatiotemporal dynamic models to predict opioid-related mortality across Massachusetts' 537 ZCTAs. We evaluated the prediction performance of our models using the one-year ahead approach. We investigated the potential improvement of prediction accuracy by incorporating ZCTA-level demographic and socioeconomic determinants. We identified ZCTAs with the highest predicted opioid-related mortality in terms of rates and counts and stratified them by rural and urban areas. RESULTS: Bayesian dynamic models with the full spatial and temporal dependency performed best. Inclusion of the ZCTA-level demographic and socioeconomic variables as predictors improved the prediction accuracy, but only in the model that did not account for the neighborhood-level spatial dependency of the ZCTAs. Predictions were better for urban areas than for rural areas, which were more sparsely populated. Using the best performing model and the Massachusetts opioid-related mortality data from 2005 through 2019, our models suggested a stabilizing pattern in opioid-related overdose mortality in 2020 and 2021 if there were no disruptive changes to the trends observed for 2005-2019. CONCLUSIONS: Our Bayesian spatiotemporal models focused on opioid-related overdose mortality data facilitated prediction approaches that can inform preemptive public health decision-making and resource allocation. While sparse data from rural and less populated locales typically pose special challenges in small area predictions, our dynamic Bayesian models, which maximized information borrowing across geographic areas and time points, were used to provide more accurate predictions for small areas. Such approaches can be replicated in other jurisdictions and at varying temporal and geographical levels. We encourage the formation of a modeling consortium for fatal opioid-related overdose predictions, where different modeling techniques could be ensembled to inform public health policy.

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BACKGROUND: A single anthropometric index such as stunting, wasting, or underweight does not show the holistic picture of under-five children's undernutrition status. To alleviate this problem, we adopted a multifaceted single index known as the composite index for anthropometric failure (CIAF). Using this undernutrition index, we investigated the disparities of Ethiopian under-five children's undernutrition status in space and time. METHODS: Data for analysis were extracted from the Ethiopian Demographic and Health Surveys (EDHSs). The space-time dynamics models were formulated to explore the effects of different covariates on undernutrition among children under five in 72 administrative zones in Ethiopia. RESULTS: The general nested spatial-temporal dynamic model with spatial and temporal lags autoregressive components was found to be the most adequate (AIC = -409.33, R2 = 96.01) model. According to the model results, the increase in the percentage of breastfeeding mothers in the zone decreases the CIAF rates of children in the zone. Similarly, the increase in the percentages of parental education, and mothers' nutritional status in the zones decreases the CIAF rate in the zone. On the hand, increased percentages of households with unimproved water access, unimproved sanitation facilities, deprivation of women's autonomy, unemployment of women, and lower wealth index contributed to the increased CIAF rate in the zone. CONCLUSION: The CIAF risk factors are spatially and temporally correlated across 72 administrative zones in Ethiopia. There exist geographical differences in CIAF among the zones, which are influenced by spatial neighborhoods of the zone and temporal lags within the zone. Hence these findings emphasize the need to take the spatial neighborhood and historical/temporal contexts into account when planning CIAF prevention.

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During the first wave of the COVID-19 pandemics in 2020, lockdown policies reduced human mobility in many countries globally. This significantly reduces car traffic-related emissions. In this paper, we consider the impact of the Italian restrictions (lockdown) on the air quality in the Lombardy Region. In particular, we consider public data on concentrations of particulate matters (PM10 and PM2.5) and nitrogen dioxide, pre/during/after lockdown. To reduce the effect of confounders, we use detailed regression function based on meteorological, land and calendar information. Spatial and temporal correlations are handled using a multivariate spatiotemporal model in the class of hidden dynamic geostatistical models (HDGM). Due to the large size of the design matrix, variable selection is made using a hybrid approach coupling the well known LASSO algorithm with the cross-validation performance of HDGM. The impact of COVID-19 lockdown is heterogeneous in the region. Indeed, there is high statistical evidence of nitrogen dioxide concentration reductions in metropolitan areas and near trafficked roads where also PM10 concentration is reduced. However, rural, industrial, and mountain areas do not show significant reductions. Also, PM2.5 concentrations lack significant reductions irrespective of zone. The post-lockdown restart shows unclear results.

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We present an approach to extend the endemic-epidemic (EE) modelling framework for the analysis of infectious disease data. In its spatiotemporal formulation, spatial dependencies have originally been captured by static neighbourhood matrices. These weight matrices are adjusted over time to reflect changes in spatial connectivity between geographical units. We illustrate this extension by modelling the spread of COVID-19 disease between Swiss and bordering Italian regions in the first wave of the COVID-19 pandemic. The spatial weights are adjusted with data describing the daily changes in population mobility patterns, and indicators of border closures describing the state of travel restrictions since the beginning of the pandemic. These time-dependent weights are used to fit an EE model to the region-stratified time series of new COVID-19 cases. We then adjust the weight matrices to reflect two counterfactual scenarios of border closures and draw counterfactual predictions based on these, to retrospectively assess the usefulness of border closures. Predictions based on a scenario where no closure of the Swiss-Italian border occurred increased the number of cumulative cases in Switzerland by a factor of 2.7 (10th to 90th percentile: 2.2 to 3.6) over the study period. Conversely, a closure of the Swiss-Italian border two weeks earlier than implemented would have resulted in only a 12% (8% to 18%) decrease in the number of cases and merely delayed the epidemic spread by a couple of weeks. Our study provides useful insight into modelling the effect of epidemic countermeasures on the spatiotemporal spread of COVID-19.

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PURPOSE OF REVIEW: Epidemiological studies of short- and long-term health impacts of ambient air pollutants require accurate exposure estimates. We describe the evolution in exposure assessment and assignment in air pollution epidemiology, with a focus on spatiotemporal techniques first developed to meet the needs of the Multi-ethnic Study of Atherosclerosis and Air Pollution (MESA Air). Initially designed to capture the substantial variation in pollutant levels and potential health impacts that can occur over small spatial and temporal scales in metropolitan areas, these methods have now matured to permit fine-scale exposure characterization across the contiguous USA and can be used for understanding long- and short-term health effects of exposure across the lifespan. For context, we highlight how the MESA Air models compare to other available exposure models. RECENT FINDINGS: Newer model-based exposure assessment techniques provide predictions of pollutant concentrations with fine spatial and temporal resolution. These validated models can predict concentrations of several pollutants, including particulate matter less than 2.5 µm in diameter (PM2.5), oxides of nitrogen, and ozone, at specific locations (such as at residential addresses) over short time intervals (such as 2 weeks) across the contiguous USA between 1980 and the present. Advances in statistical methods, incorporation of supplemental pollutant monitoring campaigns, improved geographic information systems, and integration of more complete satellite and chemical transport model outputs have contributed to the increasing validity and refined spatiotemporal spans of available models. Modern models for predicting levels of outdoor concentrations of air pollutants can explain a substantial amount of the spatiotemporal variation in observations and are being used to provide critical insights into effects of air pollutants on the prevalence, incidence, progression, and prognosis of diseases across the lifespan. Additional enhancements in model inputs and model design, such as incorporation of better traffic data, novel monitoring platforms, and deployment of machine learning techniques, will allow even further improvements in the performance of pollutant prediction models.

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Spatiotemporal models are a popular tool for urban traffic forecasting, and their correct specification is a challenging task. Temporal aggregation of traffic sensor data series is a critical component of model specification, which determines the spatial structure and affects models' forecasting accuracy. Through extensive experiments with real-world data, we investigated the effects of the selected temporal aggregation level for forecasting performance of different spatiotemporal model specifications. A set of analysed models include travel-time-based and correlation-based spatially restricted vector autoregressive models, compared to classical univariate and multivariate time series models. Research experiments are executed in several dimensions: temporal aggregation levels, forecasting horizons (one-step and multi-step forecasts), spatial complexity (sequential and complex spatial structures), the spatial restriction approach (unrestricted, travel-time-based and correlation-based), and series transformation (original and detrended traffic volumes). The obtained results demonstrate the crucial role of the temporal aggregation level for identification of the spatiotemporal traffic flow structure and selection of the best model specification. We conclude that the common research practice of an arbitrary selection of the temporal aggregation level could lead to incorrect conclusions on optimal model specification. Thus, we recommend extending the traffic forecasting methodology by validation of existing and newly developed model specifications for different temporal aggregation levels. Additionally, we provide empirical results on the selection of the optimal temporal aggregation level for the discussed spatiotemporal models for different forecasting horizons.

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Wildlife diseases pose a substantial threat to the provisioning of ecosystem services. We use a novel modeling approach to study the potential loss of these services through the imminent introduction of chronic wasting disease (CWD) to elk populations in the Greater Yellowstone Ecosystem (GYE). A specific concern is that concentrating elk at feedgrounds may exacerbate the spread of CWD, whereas eliminating feedgrounds may increase the number of elk on private ranchlands and the transmission of a second disease, brucellosis, from elk to cattle. To evaluate the consequences of management strategies given the threat of two concurrent wildlife diseases, we develop a spatiotemporal bioeconomic model. GPS data from elk and landscape attributes are used to predict migratory behavior and population densities with and without supplementary feeding. We use a 4,800 km2 area around Pinedale, Wyoming containing four existing feedgrounds as a case study. For this area, we simulate welfare estimates under a variety of management strategies. Our results indicate that continuing to feed elk could result in substantial welfare losses for the case-study region. Therefore, to maximize the present value of economic net benefits generated by the local elk population upon CWD's arrival in the region, wildlife managers may wish to consider discontinuing elk feedgrounds while simultaneously developing new methods to mitigate the financial impact to ranchers of possible brucellosis transmission to livestock. More generally, our methods can be used to weigh the costs and benefits of human-wildlife interactions in the presence of multiple disease risks.

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Typhoid fever is a global infectious disease which remains a severe health problem in Asia and Africa. In subnational levels of Iran, environmental and socio-economic properties are often so divergent, that can have a major effect on the incidence of typhoid fever. We used the data of MOHME that has reported 2474 cases of typhoid fever from 20th Feb 2012 to 31st Dec 2017 in Iran. First, we ran a spatial autocorrelation analysis to see whether there is any spatial trend in incidence cases and find the high-high clusters of typhoid (at different confidence levels) using Local indicators of spatial association (LISAs). To explore the spatial and temporal patterns of typhoid fever and examine their relationship with climatic and socio-economic variables; we have employed a spatiotemporal zero-inflated Poisson (ZIP) model in a Bayesian framework. Our results show thirteen High-High clusters and windspeed (RR [95% CrI] = 1.39 [1.15-1.69]), public sewerage system (RR [95% CrI] = 0.76 [0.63-0.92]), years of schooling (RR [95% CrI] = 0.78 [0.65-0.95]), wealth index (RR [95% CrI] = 0.59 [0.55-0.63]) and urbanization (RR [95% CrI] = 0.6 [0.48-0.76]) as variables that are importantly associated with typhoid fever incidence. Therefore, typhoid fever is spatially clustered with a high incidence in children and adolescents. Windy, poor, rural, and uneducated areas are high-risk regions that can be controlled by proliferating the standard sewerage networks, which eventually leads to safer water supplies.

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Conservation of at-risk species is aided by reliable forecasts of the consequences of environmental change and management actions on population viability. Forecasts from conventional population viability analysis (PVA) are made using a two-step procedure in which parameters are estimated, or elicited from expert opinion, and then plugged into a stochastic population model without accounting for parameter uncertainty. Recently developed statistical PVAs differ because forecasts are made conditional on models fitted to empirical data. The statistical forecasting approach allows for uncertainty about parameters, but it has rarely been applied in metapopulation contexts where spatially explicit inference is needed about colonization and extinction dynamics and other forms of stochasticity that influence metapopulation viability. We conducted a statistical metapopulation viability analysis (MPVA) using 11 yr of data on the federally threatened Chiricahua leopard frog (Lithobates chiricahuensis) to forecast responses to landscape heterogeneity, drought, environmental stochasticity, and management. We evaluated several future environmental scenarios and pond restoration options designed to reduce extinction risk. Forecasts over a 50-yr time horizon indicated that metapopulation extinction risk was <4% for all scenarios, but uncertainty was high. Without pond restoration, extinction risk is forecasted to be 3.9% (95% CI 0-37%) by year 2066. Restoring six ponds by increasing their hydroperiod reduced extinction risk to <1% and greatly reduced uncertainty (95% CI 0-2%). Our results suggest that managers can mitigate the impacts of drought and environmental stochasticity on metapopulation viability by maintaining ponds that hold water throughout the year and keeping them free of invasive predators. Our study illustrates the utility of the spatially explicit statistical forecasting approach to MPVA in conservation planning efforts.

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People are increasingly concerned with understanding their personal environment, including possible exposure to harmful air pollutants. In order to make informed decisions on their day-to-day activities, they are interested in real-time information on a localized scale. Publicly available, fine-scale, high-quality air pollution measurements acquired using mobile monitors represent a paradigm shift in measurement technologies. A methodological framework utilizing these increasingly fine-scale measurements to provide real-time air pollution maps and short-term air quality forecasts on a fine-resolution spatial scale could prove to be instrumental in increasing public awareness and understanding. The Google Street View study provides a unique source of data with spatial and temporal complexities, with the potential to provide information about commuter exposure and hot spots within city streets with high traffic. We develop a computationally efficient spatiotemporal model for these data and use the model to make short-term forecasts and high-resolution maps of current air pollution levels. We also show via an experiment that mobile networks can provide more nuanced information than an equally-sized fixed-location network. This modeling framework has important real-world implications in understanding citizens' personal environments, as data production and real-time availability continue to be driven by the ongoing development and improvement of mobile measurement technologies.

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Background: Scrub typhus is an important public health issue in Korea. Risk factors for scrub typhus include both individual-level factors and environmental drivers, and some are related to the increased density of vector mites and rodents, the natural hosts of the mites. In this regard, deforestation is a potential risk factor, because the deforestation-induced secondary growth of scrub vegetation may increase the densities of mites and rodents. To examine this hypothesis, this study investigated the association between scrub typhus and deforestation. Methods: We acquired district-level data for 2006-2017, including the number of cases of scrub typhus reported annually, deforestation level, and other covariates. Deforestation was assessed using preprocessed remote-sensing satellite data. Bayesian regression models, including Poisson, negative binomial, zero-inflated Poisson, and zero-inflated negative binomial models, were examined, and spatial autocorrelation was considered in hierarchical models. A sensitivity analysis was conducted using different accumulation periods for the deforestation level to examine the robustness of the association. Results: The final models showed a significant association between deforestation and the incidence of scrub typhus (relative risk = 1.20, 95% credible interval = 1.15-1.24). The sensitivity analysis gave consistent results, and a potential long-term effect of deforestation for up to 5 years was shown. Conclusion: The results support the potential public health benefits of forest conservation by suppressing the risk of scrub typhus, implying the need for strong engagement of public health sectors in conservation issues from a One Health perspective.

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Background: Hand, foot, and mouth disease (HFMD) is a common infectious disease among children. Guangdong Province is one of the most severely affected provinces in south China. This study aims to identify the spatiotemporal distribution characteristics and potential predictors of HFMD in Guangdong Province and provide a theoretical basis for the disease control and prevention. Methods: Case-based HFMD surveillance data from 2009 to 2012 was obtained from the China Center for Disease Control and Prevention (China CDC). The Bayesian spatiotemporal model was used to evaluate the spatiotemporal variations of HFMD and identify the potential association with meteorological and socioeconomic factors. Results: Spatially, areas with higher relative risk (RR) of HFMD tended to be clustered around the Pearl River Delta region (the mid-east of the province). Temporally, we observed that the risk of HFMD peaked from April to July and October to December each year and detected an upward trend between 2009 and 2012. There was positive nonlinear enhancement between spatial and temporal effects, and the distribution of relative risk in space was not fixed, which had an irregular fluctuating trend in each month. The risk of HFMD was significantly associated with monthly average relative humidity (RR: 1.015, 95% CI: 1.006-1.024), monthly average temperature (RR: 1.045, 95% CI: 1.021-1.069), and monthly average rainfall (RR: 1.004, 95% CI: 1.001-1.008), but not significantly associated with average GDP. Conclusions: The risk of HFMD in Guangdong showed significant spatiotemporal heterogeneity. There was spatiotemporal interaction in the relative risk of HFMD. Adding a spatiotemporal interaction term could well explain the change of spatial effect with time, thus increasing the goodness of fit of the model. Meteorological factors, such as monthly average relative humidity, monthly average temperature, and monthly average rainfall, might be the driving factors of HFMD.

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The spatial resolution of third party traffic data is not adequately describing the variation of air pollution exposure along the travelled routes of bicycle commuters. In prior work, a city-wide mobile noise mapping methodology was proposed to predict Black Carbon exposure for random bicycle trips, including meteorological variability. In a proof-of-concept pilot, funded by the National Institutes of Environmental Health Sciences (NIEHS), this method is examined in the context of a commuter study in New York City. An independent measurement campaign sampled for noise, Black Carbon and Ultrafine Particles in NYC. We focus on the spatiotemporal analysis of the preliminary data. NYC has different fleet composition compared to Ghent (i.e. less diesel, more hybrids) and different geography. Additional parameters are identified to improve the model in comparison to the prior European work. The validity, feasibility and applicability of the methodology are positively evaluated. Sampling exposure across all seasons during rush hours couldn't be reached within the pilot. Adding noise levels meters to the protocol of the commuter study can supply the missing data with minimal investments. When a full year of data becomes available, the commuter study can be retro-actively attributed with meteorology independent exposure for BC and UFP.

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Gaussian process dynamical systems (GPDS) represent Bayesian nonparametric approaches to inference of nonlinear dynamical systems, and provide a principled framework for the learning of biological networks from multiple perturbed time series measurements of gene or protein expression. Such approaches are able to capture the full richness of complex ODE models, and can be scaled for inference in moderately large systems containing hundreds of genes. Related hierarchical approaches allow for inference from multiple datasets in which the underlying generative networks are assumed to have been rewired, either by context-dependent changes in network structure, evolutionary processes, or synthetic manipulation. These approaches can also be used to leverage experimentally determined network structures from one species into another where the network structure is unknown. Collectively, these methods provide a comprehensive and flexible platform for inference from a diverse range of data, with applications in systems and synthetic biology, as well as spatiotemporal modelling of embryo development. In this chapter we provide an overview of GPDS approaches and highlight their applications in the biological sciences, with accompanying tutorials available as a Jupyter notebook from https://github.com/cap76/GPDS .

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In ecological systems, extremes can happen in time, such as population crashes, or in space, such as rapid range contractions. However, current methods for joint inference about temporal and spatial dynamics (e.g., spatiotemporal modeling with Gaussian random fields) may perform poorly when underlying processes include extreme events. Here we introduce a model that allows for extremes to occur simultaneously in time and space. Our model is a Bayesian predictive-process GLMM (generalized linear mixed-effects model) that uses a multivariate-t distribution to describe spatial random effects. The approach is easily implemented with our flexible R package glmmfields. First, using simulated data, we demonstrate the ability to recapture spatiotemporal extremes, and explore the consequences of fitting models that ignore such extremes. Second, we predict tree mortality from mountain pine beetle (Dendroctonus ponderosae) outbreaks in the U.S. Pacific Northwest over the last 16 yr. We show that our approach provides more accurate and precise predictions compared to traditional spatiotemporal models when extremes are present. Our R package makes these models accessible to a wide range of ecologists and scientists in other disciplines interested in fitting spatiotemporal GLMMs, with and without extremes.

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Targeted intervention and resource allocation are essential for effective malaria control, particularly in remote areas, with predictive models providing important information for decision making. While a diversity of modeling technique have been used to create predictive models of malaria, no work has made use of Bayesian networks. Bayes nets are attractive due to their ability to represent uncertainty, model time lagged and nonlinear relations, and provide explanations. This paper explores the use of Bayesian networks to model malaria, demonstrating the approach by creating village level models with weekly temporal resolution for Tha Song Yang district in northern Thailand. The networks are learned using data on cases and environmental covariates. Three types of networks are explored: networks for numeric prediction, networks for outbreak prediction, and networks that incorporate spatial autocorrelation. Evaluation of the numeric prediction network shows that the Bayes net has prediction accuracy in terms of mean absolute error of about 1.4 cases for 1 week prediction and 1.7 cases for 6 week prediction. The network for outbreak prediction has an ROC AUC above 0.9 for all prediction horizons. Comparison of prediction accuracy of both Bayes nets against several traditional modeling approaches shows the Bayes nets to outperform the other models for longer time horizon prediction of high incidence transmission. To model spread of malaria over space, we elaborate the models with links between the village networks. This results in some very large models which would be far too laborious to build by hand. So we represent the models as collections of probability logic rules and automatically generate the networks. Evaluation of the models shows that the autocorrelation links significantly improve prediction accuracy for some villages in regions of high incidence. We conclude that spatiotemporal Bayesian networks are a highly promising modeling alternative for prediction of malaria and other vector-borne diseases.

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