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Sika deer (Cervus nippon) populations have damaged habitats, agricultural crops, and commercial forests in many parts of the world, including Asia, Europe, northern America, and New Zealand. Population management of sika deer is an important task in those areas. To better understand large-scale management and improve management efficiency, the authors estimated spatio-temporal changes of density distribution and population dynamics of a managed population of sika deer on Kyushu Island (approximately 36,750 km2), Japan. The authors estimated these changes by using fecal pellet count surveys conducted from 1995 to 2019 and results from a vector autoregressive spatio-temporal model. No decreasing trend of populations were observed at the island and prefectural scales, even though the management goal has been to reduce the population by half, and harvesting on the island increased annually until it reached about 110,000 sika deer in 2014. A possible explanation for the stable population dynamics is that the population used to determine the harvest number under the prefectural management plan was originally underestimated. This study highlights not only the difficulties of wide-area management of sika deer but also three important factors for successful management: reducing the risk of management failure, using an adaptive management approach, and appropriate management scale.

Landslide represents an increasing menace causing huge casualties and economic losses, and rainfall is a predominant factor inducing landslides. Landslide susceptibility assessment (LSA) is a commonly used and effective method to prevent landslide risk, however, the LSA does not analyze the impact of the rainfall on landslides which is significant and non-negligible. Therefore, the spatiotemporal LSA considering the inducing effect of rainfall is proposed to improve accuracy and applicability. In this study, the influencing factors are selected using the chi-square test, out-of-bag error and multicollinearity test. The spatial LSA are thus obtained using the random forest (RF) model, deep belief networks model and support vector machine, and compared using receiver operating characteristic curve and seed cell area index to determine the optimal assessment result. According to the heavy rainfall characteristics in the study area, the rainfall period is divided into four stages, and the effective rainfall model is employed to generate the rainfall impact (RI) maps of the four stages. The spatiotemporal LSAs are obtained by coupling the optimal spatial LSA and various RI maps and verified using the landslide warning map. The results demonstrate that the optimal spatiotemporal LSA is obtained using the spatial LSA of the RF model and temporal LSA of the rainfall data in the peak stage. It can predict the area where rainfall-induced landslides are likely to occur and prevent landslide risk.

Basketball games evolve continuously in space and time as players constantly interact with their teammates, the opposing team, and the ball. However, current analyses of basketball outcomes rely on discretized summaries of the game that reduce such interactions to tallies of points, assists, and similar events. In this article, we propose a framework for using optical player tracking data to estimate, in real time, the expected number of points obtained by the end of a possession. This quantity, called expected possession value (EPV), derives from a stochastic process model for the evolution of a basketball possession. We model this process at multiple levels of resolution, differentiating between continuous, infinitesimal movements of players, and discrete events such as shot attempts and turnovers. Transition kernels are estimated using hierarchical spatiotemporal models that share information across players while remaining computationally tractable on very large data sets. In addition to estimating EPV, these models reveal novel insights on players' decision-making tendencies as a function of their spatial strategy. In the supplementary material, we provide a data sample and R code for further exploration of our model and its results.

Radar echo maps are essential for precipitation forecasting, providing visual representations of rainfall patterns, including spatial distribution and intensity. To enhance radar echo prediction, this study introduces the MSIM–MIM model, which integrates the MFEF and SIM modules within the MIM framework. The MFEF module utilizes dilated convolutions to capture multi‐scale features while maintaining spatial details, improving contextual understanding, and boosting prediction accuracy, all without increasing computational cost. The SIM module employs a gating mechanism to selectively extract and process spatiotemporal context, thereby enhancing the model's ability to represent these patterns. This results in more refined state representations, allowing the MSIM–MIM model to retain and leverage context more effectively, thus reducing prediction errors. Experimental results demonstrate that MSIM–MIM outperforms other spatiotemporal models, achieving lower MSE and MAE in radar echo predictions across multiple datasets. The SIM module enhances spatiotemporal prediction by extracting both temporal and spatial context information through nonlinear mappings. It improves the model's ability to capture context and facilitates interactions between multi‐state inputs; thereby reducing prediction errors, particularly in radar echo maps.

Spatial epidemiology investigates the patterns and determinants of health outcomes over both space and time. Within this field, Bayesian spatiotemporal models have gained popularity due to their capacity to incorporate spatial and temporal dependencies, uncertainties, and intricate interactions. However, the complexity of modelling and computations associated with Bayesian spatiotemporal models vary across different diseases. Presently, there is a limited comprehensive overview of Bayesian spatiotemporal models and their applications in epidemiology. This article aims to address this gap through a thorough review. The review commences by delving into the historical development of Bayesian spatiotemporal models concerning disease mapping, prediction, and regression analysis. Subsequently, the article compares these models in terms of spatiotemporal data distribution, general spatiotemporal data models, environmental covariates, parameter estimation methods, and model fitting standards. Following this, essential preparatory processes are outlined, encompassing data acquisition, data preprocessing, and available statistical software. The article further categorizes and summarizes the application of Bayesian spatiotemporal models in spatial epidemiology. Lastly, a critical examination of the advantages and disadvantages of these models, along with considerations for their application, is provided. This comprehensive review aims to enhance comprehension of the dynamic spatiotemporal distribution and prediction of epidemics. By facilitating effective disease scrutiny, especially in the context of the global COVID-19 pandemic, the review holds significant academic merit and practical value. It also aims to contribute to the development of improved ecological and epidemiological prevention and control strategies.

Particulate matter poses significant risks to respiratory and cardiovascular health. Monitoring ambient particulate matter concentrations can provide information on potential exposures and inform mitigation strategies, but ground-based measurements are sparse. Data fusion approaches that integrate data from multiple sources can complement existing observation networks and reveal insights that single-sensor data might miss to better manage pollutant exposure risks. However, data fusion approaches face multiple challenges, including incompatible measurement units, varying data resolutions, and differing levels of uncertainty. As a result, the optimal method for data fusion remains an open question. Here, we propose a probabilistic spatiotemporal model, based on the stochastic advection–diffusion (SAD) equation, as a data fusion method to process multimodal air quality data to predict hourly concentrations of fine particulate matter (PM2.5). We employ a variational inference method to calibrate the probabilistic model using ground-level observations and the numerical output of two simulation models. We then evaluate the prediction performance of our model for two scenarios: (1) incorporating simulation outputs and ground-level observations from sparse regulatory-grade stations and (2) using ground-level observations from both low-cost and regulatory-grade stations. For the first scenario, the data fusion method reduces prediction error by 14% compared to the nearest regulatory-grade air monitor located 20 km away. For the second scenario, error is reduced by 40% compared to the nearest regulatory-grade monitor and 11% compared to the nearest low-cost sensor located approximately 1 km away. The model captures 78% of observed data within a 75% confidence interval across both scenarios, demonstrating its ability to accurately represent uncertainty. Our findings demonstrate that the proposed SAD model can effectively integrate multimodal data to provide improved prediction of particulate matter concentrations at high spatial resolution. Model outputs can inform individual and community-level decision-making to mitigate air pollutant exposures.

Nowadays, air pollution is an important problem with negative impacts on human health and on the environment. The air pollution forecast can provide important information to all affected sides, and allows appropriate measures to be taken. In order to address the problems of filling in the missing values in the time series used for air pollution forecasts, the automation of the allocation of optimal subset of input variables, the dependency of the air quality at a particular location on the conditions of the surrounding environment, as well as automation of the model’s optimization, this paper proposes a deep spatiotemporal model based on a 2D convolutional neural network and a long short-term memory network for predicting air pollution. The model utilizes the automatic selection of input variables and the optimization of hyperparameters by a genetic algorithm. A hybrid strategy for missing value imputation is used based on a combination of linear interpolation and a strategy of using the average between the previous value and the average value for the same time in other years. In order to determine the best architecture of the spatiotemporal model, the architecture hyperparameters are optimized by a genetic algorithm with a modified crossover operator for solutions with variable lengths. Additionally, the trained models are included in various ensembles in order to further improve the prediction performance—these include ensembles of models with the same architecture comprising the best architecture obtained by the evolutionary optimization, and ensembles of diverse models comprising the k best models of the evolutionary optimization. The experimental results for the Beijing Multi-Site Air-Quality Data Set show that the proposed spatiotemporal model for air pollution forecasting provides good and consistent prediction results. The comparison of the suggested model with other deep NN models shows satisfactory results, with the best performance according to MAE, based on the experimental results for the station at Wanliu (16.753 ± 0.384). Most of the model architectures obtained by the optimization of the model hyperparameters using the genetic algorithm have one convolutional layer with a small number of kernels and a small kernel size; the convolutional layers are followed by a max-pooling layer, and one or two LSTM layers are utilized with dropout regularization applied to the LSTM layer using small values of p (0.1, 0.2 and 0.3). The utilization of ensembles from the k best trained models further improves the prediction results and surpasses other deep learning models, according to MAE and RMSE metrics. The used hybrid strategy for missing value imputation enhances the results, especially for data with clear seasonality, and produces better MAE compared to the strategy using average values for the same hour of the same day and month in other years. The experimental results also reveal that random searching is a simple and effective strategy for selecting the input variables. Furthermore, the inclusion of spatial information in the model’s input data, based on the local neighborhood data, significantly improves the predictive results obtained with the model. The results obtained demonstrate the benefits of including spatial information from as many surrounding stations as possible, as well as using as much historical information as possible.

Many distributed parameter systems (DPSs) have strongly nonlinear spatiotemporal dynamics, unknown parameters and complex boundary conditions, which make it difficult to obtain accurate prediction and control in actual practice. In this paper, a data-driven spatiotemporal model predictive control (MPC) strategy is proposed for nonlinear DPSs. It first develops a low-order nonlinear spatiotemporal model by using kernel principal component analysis to reconstruct the nonlinear spatial dynamics, so that the spatial nonlinearity is better reserved in contrast with the traditional data-driven DPS modeling methods. On this basis, a spatiotemporal MPC is proposed for nonlinear DPSs. In this control strategy, a new objective function is constructed with consideration of errors on not only time but also space, which overcomes the shortcoming of the traditional MPC due to the ignorance of nonlinear spatial dynamics. The stability and effectiveness of the proposed spatiotemporal control strategy are demonstrated by mathematical stability and comparative case studies.

Increasingly larger data sets of processes in space and time ask for statistical models and methods that can cope with such data. We show that the solution of a stochastic advection–diffusion partial differential equation provides a flexible model class for spatiotemporal processes which is computationally feasible also for large data sets. The Gaussian process defined through the stochastic partial differential equation has, in general, a non‐separable covariance structure. Its parameters can be physically interpreted as explicitly modelling phenomena such as transport and diffusion that occur in many natural processes in diverse fields ranging from environmental sciences to ecology. To obtain computationally efficient statistical algorithms, we use spectral methods to solve the stochastic partial differential equation. This has the advantage that approximation errors do not accumulate over time, and that in the spectral space the computational cost grows linearly with the dimension, the total computational cost of Bayesian or frequentist inference being dominated by the fast Fourier transform. The model proposed is applied to post‐processing of precipitation forecasts from a numerical weather prediction model for northern Switzerland. In contrast with the raw forecasts from the numerical model, the post‐processed forecasts are calibrated and quantify prediction uncertainty. Moreover, they outperform the raw forecasts, in the sense that they have a lower mean absolute error.

Background Brucellosis shows pronounced spatiotemporal heterogeneity in China, with changing epidemiological patterns as traditionally non-endemic southern regions experience increasing incidence. This study analyzes the spatiotemporal distribution and influencing factors of brucellosis in China to inform differentiated prevention strategies. Methods Using human brucellosis data from 31 Chinese provinces (2004–2021), combined with meteorological, socioeconomic, and livestock husbandry indicators, we developed Bayesian spatiotemporal models to analyze provincial-level spatial effects, temporal effects, spatiotemporal interactions, and quantify the impact of multiple factors on brucellosis incidence risk at the provincial scale. Richardson classification was applied for hotspot analysis, and average annual percentage change (AAPC) evaluated incidence trends. Results China reported 687,529 brucellosis cases (2004–2021). Spatial distribution showed a “high north, low south” pattern, with Inner Mongolia having the highest incidence (45.81/100,000) and Shanghai the lowest (0.01/100,000). Northern regions contained most hotspots (41.94%), while southern areas comprised most coldspots (51.61%). Temporal analysis revealed increasing risk (2004–2016), brief decline (2016–2018), and subsequent increase (post-2018). Spatiotemporal interaction effects indicated provincial-level risk pattern shifts from northern to central-southern regions, with Gansu, Hubei, Yunnan, and Hunan showing highest growth (AAPCs: 64.42%, 53.80%, 53.61%, 50.47%). Ecological regression identified six significant factors: mean temperature, sunshine duration, NDVI, population density, and medical institutions density negatively correlated with risk; dairy production positively associated with risk. Conclusions At the provincial level, brucellosis risk patterns in China show shifts from traditional northern high-incidence provinces to central-southern provinces. Environmental, socioeconomic, and livestock factors significantly influence disease risk. Prevention strategies should implement region-specific approaches while strengthening multi-departmental coordination.