Extreme Value Theory (EVT) provides a logical framework for estimating crash risk by extrapolating from observed traffic conflicts to rare crashes. Bayesian hierarchical extreme value (BHEV) models address the scarcity of extreme conflicts by pooling information across sites, but most applications overlook spatial correlation. This study extends the BHEV framework by incorporating conditional autoregressive (CAR) priors and comparing spatial models with site-specific random-intercept models. A Besag-York-Mollié 2-style reparameterization is employed to address identifiability between structured and unstructured variance components. Using drone-derived trajectory data from an urban network in Athens, Greece, CAR and intrinsic CAR models were fitted and outperformed the random-intercept model. The results showed statistically significant spatial correlation and strong tail fit under multiple backtesting procedures, including unconditional coverage, conditional coverage, and dynamic quantile tests. Spatial priors also meaningfully changed crash risk estimates and site prioritisation, demonstrating the value of modelling spatial dependence in network-level conflict-based crash risk prediction.

Oral squamous cell carcinomas (OSCC), the predominant head and neck cancer, pose significant challenges due to late-stage diagnoses and low five-year survival rates. Spatial transcriptomics offers a promising avenue to decipher the genetic intricacies of OSCC tumor microenvironments. In spatial transcriptomics, Cell-type deconvolution is a crucial inferential goal; however, current methods fail to consider the high zero-inflation present in OSCC data. To address this, we develop a novel zero-inflated version of the hierarchical generalized transformation model (ZI-HGT) and apply it to the Conditional AutoRegressive Deconvolution (CARD) for cell-type deconvolution. The ZI-HGT serves as an auxiliary Bayesian technique for CARD, reconciling the highly zero-inflated OSCC spatial transcriptomics data with CARD's normality assumption. The combined ZI-HGT + CARD framework achieves enhanced cell-type deconvolution accuracy and quantifies uncertainty in the estimated cell-type proportions. We demonstrate the superior performance through simulations and analysis of the OSCC data. Furthermore, our approach enables the determination of the locations of the diverse fibroblast population in the tumor microenvironment, critical for understanding tumor growth and immunosuppression in OSCC.

We investigate the ecological and evolutionary variables that best explain spatial diversity patterns of anuran amphibians in three of South America's most diverse and geographically widespread biomes: the Cerrado, Amazonia, and Atlantic Rainforest. We used Conditional Autoregressive Models to assess the potential influence of present-day climate (temperature and precipitation), historical climate (stability over the last 120,000 years), potential evapotranspiration (PET), and topography (slope, aspect, and rugosity) on spatial variation in taxonomic, functional, and phylogenetic diversity at a resolution of 0.5 × 0.5 degrees. Both taxonomic diversity and phylogenetic diversity increased with long-term climatic stability in all regions. By contrast, functional diversity was negatively impacted by precipitation in the driest quarter. However, the relative importance of each predictor variable differed among diversity metrics and biomes. In the Atlantic Rainforest, potential evapotranspiration was positively correlated with functional diversity but negatively associated with taxonomic and phylogenetic diversity. In Amazonia, precipitation and relief slopes were positively associated with functional and phylogenetic diversity, respectively, whereas relief slopes were negatively correlated with taxonomic diversity. In the Cerrado, precipitation was negatively correlated with functional diversity, but climatic stability was more strongly associated with phylogenetic and taxonomic diversity. These findings indicate that present-day climatic factors are critical in forested biomes, whereas a combination of historical and current variables is more relevant in Cerrado's savanna mosaics. Notably, ecotones exhibit significantly higher functional diversity (except for Amazon), reflecting the encounter of faunas from adjacent biomes having distinct ecological regimes and thus associated organismal traits. Characterizing the drivers of heterogeneous biodiversity distribution will offer insights into the assembly of ecological communities in other tropical and transitional ecosystems and can potentially guide conservation strategies globally.

Dengue Hemorrhagic Fever (DHF) remains a significant public health challenge in Indonesia, including in Makassar City, which reported an increase of 291 cases in 2024. This study aimed to estimate the relative risk of DHF across 15 districts of Makassar by incorporating covariates such as population density, distance to the city center, and the number of hospitals, using a Bayesian Conditional Autoregressive (CAR) Localised approach. The data were obtained from the publication Makassar City in Figures 2025, issued by the Central Statistics Agency. Spatial autocorrelation analysis with Moran’s I indicated significant clustering of DHF cases. Model selection was conducted using the Deviance Information Criterion (DIC), Watanabe–Akaike Information Criterion (WAIC), and group-level area coverage. The results showed that the best-fitting model was the CAR Localised model with distance as a covariate (M9), specified at G = 3 with hyperprior IG (1; 0.01). Distance exhibited a negative association with DHF incidence, suggesting that the farther a district is from the city center, the lower its relative risk. Among the districts, Rappocini exhibited the highest relative risk followed by Panakkukang, while the lowest risks were observed in Sangkarrang Islands. These findings provide valuable insights for designing spatially targeted DHF prevention and control strategies in Makassar City.

Oral squamous cell carcinomas (OSCC), the predominant head and neck cancer, pose significant challenges due to late-stage diagnoses and low five-year survival rates. Spatial transcriptomics offers a promising avenue to decipher the genetic intricacies of OSCC tumor microenvironments. In spatial transcriptomics, Cell-type deconvolution is a crucial inferential goal; however, current methods fail to consider the high zero-inflation present in OSCC data. To address this, we develop a novel zero-inflated version of the hierarchical generalized transformation model (ZI-HGT) and apply it to the Conditional AutoRegressive Deconvolution (CARD) for cell-type deconvolution. The ZI-HGT serves as an auxiliary Bayesian technique for CARD, reconciling the highly zero-inflated OSCC spatial transcriptomics data with CARD's normality assumption. The combined ZI-HGT + CARD framework achieves enhanced cell-type deconvolution accuracy and quantifies uncertainty in the estimated cell-type proportions. We demonstrate the superior performance through simulations and analysis of the OSCC data. Furthermore, our approach enables the determination of the locations of the diverse fibroblast population in the tumor microenvironment, critical for understanding tumor growth and immunosuppression in OSCC.

Real world spatio-temporal datasets, and phenomena related to them, are often challenging to visualise or gain a general overview of. In order to summarise information encompassed in such data, we combine two well known statistical modelling methods. To account for the spatial dimension, we use the intrinsic modification of the conditional autoregression, and incorporate it with the hidden Markov model, allowing the spatial patterns to vary over time. We apply our method to parish register data considering deaths caused by measles in Finland in 1750–1850, and gain novel insight of previously undiscovered infection dynamics. Five distinctive, reoccurring states, describing spatially and temporally differing infection burden and potential routes of spread, are identified. We also find that there is a change in the occurrences of the most typical spatial patterns circa 1812, possibly due to changes in communication networks after major administrative transformations in Finland.

This paper presents a Bayesian spatio-temporal model with space-time interaction effects for longitudinal data. The main objective is to evaluate how spatial and temporal dependencies, together with their interactions, influence parameter estimation and interpretation. The model incorporates spatial random effects to capture unobserved heterogeneity between neighboring regions, temporal random effects to reflect trends over time, and interaction terms to account for localized space-time variations. A conditional autoregressive (CAR) prior is applied to address spatial dependence, while Markov chain Monte Carlo (MCMC) sampling is used for posterior estimation, supported by convergence diagnostics such as trace plots and the Geweke test. Bootstrap analysis is also applied to assess the stability of estimates and provide complementary validation. Results based on simulated datasets across multiple areal unit sizes show that the intercept and covariate effects are sensitive to spatial resolution, whereas spatial and temporal correlations remain relatively stable across scales. The variance components, particularly the interaction term, capture localized heterogeneity more effectively at smaller spatial units. The findings demonstrate that combining Bayesian estimation with bootstrap analysis provides a reliable framework for understanding spatial and temporal disease dynamics, with practical implications for public health planning and intervention strategies.

Rainfall in East Java has high spatial variation, requiring a modeling approach that can capture inter-regional dependencies. This study aims to estimate rainfall patterns using Bayesian Conditional Autoregressive (BCAR) models that incorporate spatial effects, specifically the Intrinsic Conditional Autoregressive (ICAR) and Leroux CAR specifications. Parameter estimation was conducted using Markov Chain Monte Carlo (MCMC) methods to ensure convergence and posterior stability. Monthly rainfall data from East Java during the 2022–2023 were analyzed by dividing the period into the transition to the rainy season (September–November) and the rainy season (December–February). The results indicate that during the rainy season, most climatic variables, including temperature, humidity, wind direstion, and cloud cover, do not show statistically significant effects on rainfall, whereas during the transition season,wind exhibits a significant positive influence. Comparative model evaluation reveals that the ICAR model provides the best predictive performance, as indicated by the lowest Root Mean Square Error (RMSE), while the Leroux CAR model demonstrates consistent estimation of spatial dependence across both periods. Simulation results further confirm that the parameter estimators are unbiased, as evidenced by the close agreement between simulated parameters and empirical data estimates. These findings demonstrate that BCAR models, particularly the ICAR specification, are effective in capturing spatial rainfall variability in East Java. This study contributes methodologically to spatial climatological analysis and provides a foundation for future research incorporating additional covariates and extended temporal coverage to enhance rainfall prediction accuracy.

Exchange rate volatility continues to shape global economies in profound ways, affecting everything from international trade and investment decisions to overall financial stability as markets become more interconnected. While researchers have produced a wealth of studies—building on classics like Purchasing Power Parity and relying heavily on tools such as Generalized Autoregressive Conditional Heteroskedasticity (GARCH) and Vector Autoregression (VAR) models—few have stepped back to map the entire field systematically. This study applied a bibliometric review to examine the exchange rate volatility knowledge base. The data was collected from the Scopus Database, including a sample set of 336 articles based on Preferred Reporting Items for Systematic reviews and Meta-Analyses (PRISMA)'s systematic review techniques. The findings show that there has been increasing interest in this research area, evidenced by the increase in articles published. Based on this analysis, the United States, the United Kingdom, and Germany are the most prolific in providing information to the research on exchange rate fluctuations by way of articles published in the three peer-reviewed journals most commonly referenced: the Journal of Econometrics, the Journal of International Money and Finance, and the Journal of forecasting. Several gaps were uncovered, such as research published on emerging countries, the limited number of collaboration networks that exist between some authors (and countries), and new areas of research that are gaining importance in the evolving financial markets, including digital currencies and innovations in fintech. By delivering a clear, visually engaging overview, this review solidifies the knowledge base on exchange rate volatility and inspire more inclusive, innovative, and practically relevant future work. In view of this, researchers should expand studies on exchange rate volatility to underexplored regions, especially Africa and Latin America, to better understand institutional and economic influences. Incorporating advanced methods like machine learning and big data analytics can enhance prediction models and practical applications of exchange rate volatility theory in global contexts.

Bovine anaplasmosis, caused by the rickettsia Anaplasma marginale, is an economically important and globally distributed tick- and blood-borne disease of cattle. Although cases are known to be widespread in Missouri, current spatiotemporal trends, presence of high-risk areas, and any potential drivers for disease trends in Missouri are poorly documented. To address these knowledge gaps, this study analyzed spatiotemporal patterns of annual, county-level anaplasmosis case counts using a Bayesian hierarchical framework. Seropositive cases of anaplasmosis detected at the University of Missouri Veterinary Medical Diagnostic Laboratory (n = 1,944) between the years 2010-2021 were used to construct data-driven Bayesian hierarchical models. All the models consisted of imputation sub-models to alleviate issues related to missing observations from spatiotemporal units (114 counties and 1 independent city, 12 years). Three progressively complex models with different assumptions for capturing the spatial, temporal, and spatiotemporal interactions that explained the variability in case counts were prepared. Model-1 included linear predictors decomposed into structured and unstructured terms for the temporal and spatial processes. Model-2 included separate temporal terms for smoothing each spatial entity and spatial smoothing terms for each temporal entity. This model was extended in Model-3, which included space-time interaction effect using first-order conditional autoregressive (CAR) priors. Based on the Deviance Information Criterion (DIC), Model 3 was superior at explaining space/time variability in the detected seropositive cases of bovine anaplasmosis. These findings indicate that distribution and risk of bovine anaplasmosis seroprevalence in Missouri are non-uniform, and potentially driven by environmental and/or management factors, operating at local and regional scales, that when identified could inform mitigation strategies.

Introduction: Lung cancer is a leading cause of cancer deaths in the U.S., with significant geographic disparities in incidence and mortality. Understanding the relationship between spatial variations and other risk factors to lung cancer mortality counts (LCMC) is critical for guiding targeted public health interventions.Objective: This study examines how spatial variations, demographic, socioeconomic, behavioral, health, and environmental risk factors are associated with LCMC in Kansas.Methods: LCMC data from 105 Kansas counties were analyzed using Poisson and Negative Binomial models incorporating Conditional Autoregressive (CAR) and Besag–York-Mollié 2 (BYM2) spatial effects models. Predictors included elderly population (%), rurality, poverty, housing, smoking, obesity, pollution, and proximity to coal power plants. Model performance was assessed using Deviance Information Criterion and the Mean Absolute Percentage Error.Results: The Poisson BYM2 model with correlated heterogeneity provided the best overall performance. In this model, the elderly population (%) and rurality were significantly and positively associated while PM2.5 showed an unexpected negative association.Conclusion: Spatial models, particularly BYM2, provide valuable insights into LCMC hotspots and risk factors. Public health strategies should focus on equity in high-risk clusters through targeted interventions and improved access to healthcare.

Malaria is a major public health challenge in sub-Saharan Africa, with transmission patterns that vary significantly across space and time due to environmental, socioeconomic, and epidemiological factors. These variations complicate efforts to design effective and targeted interventions, making it crucial to understand the dynamics of disease spread. This study employed Bayesian spatio-temporal random effects modeling framework to analyze malaria incidence and mortality ratio across Kenya. The approach incorporated spatial and temporal dependencies to provide a detailed understanding of malaria incidence and mortality risk patterns. Spatial random effects were modeled using conditional autoregressive (CAR) priors to account for correlations among neighboring counties, while temporal dependence was captured using autoregressive processes of order two (AR2), reflecting trends over multiple time periods. An evaluation was on the performance of Spatio-Temporal Poisson Linear Trend Model (STPLM), Spatio-Temporal Poisson ANOVA Model (STPAM), Spatio-Temporal Poisson Separable Model (STPSM) and Poisson Temporal Model for Spatio-Temporal Effects (PTSTN)using the Deviance Information Criterion (DIC), the effective number of parameters (p.d) and the Log Marginal Pseudo-Likelihood (LMPL). The Spatio-Temporal Poisson ANOVA Model (STPAM) was found as the best Poissson Spatial-Temporal Model and was used to develop a multivariate spatio-temporal model for the joint modeling of malaria incidence and mortality. Using the developed model, the study identified significant spatial clustering of malaria, with persistent high-risk zones in western and coastal counties. Temporal trends indicated an overall decline in transmission, though progress was uneven across counties, reflecting differences in intervention coverage, healthcare access, and local epidemiology. These findings underscored the value of multivariate spatio-temporal modeling of malaria incidence and mortality for guiding malaria control strategies. This study thus demonstrates that Bayesian Spatial-Temporal modeling is essential for understanding heterogeneous malaria incidence and mortality risk and informing strategies aimed at reducing disease burden and advancing toward malaria elimination in Kenya.

Pan-Homophonic events denote fluctuations in stock prices that are triggered by phonetic similarities between event keywords and stock tickers. As a relatively novel and under-researched phenomenon, they mirror a subtle yet influential behavioral deviation within financial markets. Centering on the case of Chuandazhisheng, this study delves into how such events produce dynamic and time-varying impacts on stock prices. A linguistic amplitude segmentation method is devised to discriminate between high- and low-intensity events based on information entropy. To separate pan-homophonic-driven price movements from broader market trends, the Relational Stock Ranking (RSR) model is integrated with a Dynamic Conditional Correlation-Generalized Autoregressive Conditional Heteroskedasticity (DCC-GARCH) framework to establish an adjusted price benchmark. The empirical analysis reveals a sequential price response: initial moderate fluctuations in the low-amplitude phase often yield to more prominent volatility in the high-amplitude phase. While price surges typically occur within one or two days of the event, they generally revert within approximately three weeks. Moreover, repeated exposures to homo- phonic stimuli seem to attenuate the response, indicating a decaying spillover pattern. These findings contribute to a more profound understanding of the intersection between linguistic cues and market behavior and provide practical insights for investor education, information filtering, and regulatory supervision.

Anal cancer mortality has increased across high-income countries, yet subnational patterns remain poorly characterized. This study provides the first comprehensive, sex-stratified, spatiotemporal analysis of anal cancer (ICD-10 C21) mortality in Spain from 1999 to 2023. We conducted an ecological, descriptive, province-level analysis of mortality using data from the National Institute of Statistics. Sex-stratified Bayesian hierarchical models were applied to estimate smoothed relative risks (RRs) by province and year, incorporating spatial, temporal, and interaction effects. Model selection was guided by the Deviance Information Criterion and Widely Applicable Information Criterion. Posterior probabilities (PP) were used to identify high-risk provinces (PP > 0.95). Among 160 candidate models, optimal structures differed by sex: males showed intrinsic Conditional Autoregressive (iCAR) spatial prior with RW1 temporal prior and Type IV interaction; females showed iCAR with RW2 temporal prior and Type III interaction. Mortality rose in both sexes: male RR increased steadily to 1.39 in 2023; female RR followed a nonlinear trajectory with delayed surge to 1.30. Variance decomposition indicated male mortality was mainly temporal (80.2%), female mortality largely spatial (58.1%). Male hotspots clustered in southern/insular provinces (e.g., Las Palmas RR=1.22, Cádiz 1.18, Valencia 1.18); female hotspots were more dispersed (e.g., Las Palmas 1.34, Málaga 1.33, Barcelona 1.26). Anal cancer mortality in Spain is rising, revealing persistent sex-specific and geographic inequalities beyond national temporal trends. Precision prevention-via gender-neutral HPV vaccination, targeted screening, and prioritization of hotspot provinces-is urgently needed.

This study employs the “Dynamic Conditional Correlation-Generalized Autoregressive Conditional Heteroskedasticity Connectedness” model to analyze stock market interconnectedness among Belt and Road countries. Building on existing literature, it extends the conclusions of previous research. The findings reveal a strong and relatively stable correlation between the stock markets of the fifteen member countries of the Belt and Road Initiative. In particular, during public emergencies, these markets exhibit stronger volatility correlation and heightened risk linkage Nevertheless, the interconnectedness remains generally stable, with market spillovers recovering swiftly even in the face of unexpected events. As the world’s second largest economy, China plays a pivotal role in the Belt and Road Initiative, particularly in ensuring the stability of the region’s stock market.

The impact of external shocks on macroeconomic fluctuations holds significant practical importance for enhancing the economic resilience of developing countries and promoting financial openness. This paper employs a Panel Conditional Homogeneous Vector Autoregression model with exogenous variables (PCHVAR-X) to investigate the internal and external determinants of macroeconomic fluctuations in emerging market economies at different stages of financial openness. The results show that global demand shocks are the most dominant external factor, accounting for approximately 30% of global output variation in both the short and long term. Among domestic factors, financial market pressure is the most significant driver of volatility. In the short term, domestic shocks contribute over 80% to macroeconomic fluctuations, but the influence of external shocks intensifies over time, such as rising from 8.41% at a financial openness level of 50% in the short term to 34.85% in the long term. The response to global monetary policy tightening exhibits an inverted "V"-shaped pattern, with initial mitigation followed by intensified volatility due to liquidity constraints. Additionally, variance decomposition indicates that commodity supply shocks contribute up to 45% to long-term commodity price volatility. The findings underscore that financial openness amplifies the effects of global shocks while also modifying the transmission mechanisms of domestic risks. These insights provide valuable guidance for emerging economies to design differentiated policy strategies balancing openness, resilience, and macroeconomic stability.

Conditional Autoregressive (CAR) models have been widely used in various disciplines, including epidemiological studies. The application of the CAR model in epidemiological studies is often associated with the relative risk of an infectious disease. This relative risk value can be estimated using the CAR models. Here, we evaluate four commonly used CAR models: the Intrinsic CAR, the Besag-York-Mollié CAR (BYM CAR), the BYM-modified CAR (BYM2 CAR), and the Leroux CAR (LCAR). To estimate CAR model parameters, Bayesian inference and the Integrated Nested Laplace Approximation (INLA) concept are used. The selected model was then used to model the number of dengue hemorrhagic fever (DHF) cases in Central Java Province in 2024. To support this analysis, we used 50 datasets simulated for each sample size (n), ranging from 10 to 100. The results of the study showed that of the four models compared, the best model was BYM2. This model was then used to model DHF cases in 2024 in Central Java Province. The research findings indicate the necessity of controlling population density, optimizing the role of medical personnel, and preparing for increased rainfall to curb the spread of dengue fever. Comprehensive detection and control measures through medical facilities are also required. Meanwhile, based on the coefficient of the altitude variable in the model, altitude has a positive influence on the number of dengue fever cases. Therefore, the conflicting conclusions between the model results and the medical perspective require data verification and further study of this variable.

Stunting remains a persistent public health issue in Indonesia, exhibiting significant spatial and temporal variation. To address this, we employed a hierarchical Bayesian spatio-temporal localized Conditional Autoregressive (CAR) model that includes a clustering component to identify risk factors and estimate relative risk (RR) across 34 provinces from 2020 to 2022. A total of 480 models were evaluated, encompassing three variants of the Bayesian spatio-temporal localized CAR model, 32 covariate combinations, and five hyperprior settings. Assuming a Poisson likelihood for stunting counts, the optimal model was estimated using Markov Chain Monte Carlo methods and included two covariates, namely the poverty rate and the incidence of low birth weight, with up to five spatial clusters. Higher poverty levels and increased prevalence of low birth weight were significantly associated with elevated stunting risk among children under five. Spatio-temporal clustering patterns and the estimated relative risks of stunting varied across Indonesian provinces from 2020 to 2022. Nusa Tenggara Timur consistently ranked among the top three provinces with the highest risk (RR = 2.421 in 2020; 2.384 in 2021; 2.676 in 2022). The highest risk was observed in Sulawesi Barat in 2022 (RR = 2.768), while DKI Jakarta consistently showed the lowest (RR = 0.004). Some key points of the article are:•Bayesian spatio-temporal models facilitate the classification of distinct area groups•The models were employed to analyze stunting patterns in Indonesia.•The inclusion of covariates influenced the number of groups identified.

Abstract This study makes a comparative assessment of the relation between four waves of the COVID-19 pandemic and the stock market in Poland. We utilize the Autoregressive Moving Average-Asymmetric Dynamic Conditional Correlation-Generalized Autoregressive Conditional Heteroskedasticity models to depict the dynamic conditional correlations between Polish stock market and the US stock market. We use the wavelet approach to investigate the time-frequency connectedness between the COVID-19 pandemic and the stock markets. The sample used covers the period from 02.01.2019 to 04.04.2022. Our findings reveal a significant relation between pandemic variables and stock market. This evidence is more pronounced in the first and second wave of infections. In contrast, the impact was considerably smaller during the third and fourth waves.

Spatial prediction of environmental suitability for vector-borne disease transmission is crucial for public health, with spatial connectivity being a critical factor. However, existing models often face a trade-off between model interpretability and the accurate representation of spatial connectivity. Simpler, interpretable models tend to oversimplify connectivity, while more advanced models can lack interpretability and often rely on difficult-to-obtain fine-grained mobility data. To address this challenge, this paper proposes an integrated framework (GES-SC) for the spatial prediction of environmental suitability for vector-borne disease transmission, which combines Geographical Environmental Similarity (GES) with quantified Spatial Connectivity (SC). The method operates on the principle that environmentally similar and highly spatially connected locations have similar transmission potential. It quantifies connectivity using available road network data and distance decay, providing an effective alternative to direct mobility data. A case study in Guangzhou, China, demonstrates that integrating this quantified spatial connectivity enhances prediction accuracy. Compared to Geographically Weighted Regression, Bayesian Conditional Autoregressive, XGBoost, and a Simple Neural Network, the GES-SC method performed better in cross-validation, achieving lower RMSE and MAE, and a higher R2. The proposed framework effectively addresses the accuracy-interpretability trade-off, improving spatial epidemiological prediction accuracy and providing an uncertainty measure for public health decisions.