Traditionally, endemic diseases such as dengue, diarrhea, and tuberculosis are modeled separately, which leads to a limited understanding of current disease dynamics and an inaccurate evaluation of the parameters of the different models. In this study, we propose a joint spatiotemporal model to predict the risks of multiple endemic diseases and identify hotspots. The model includes spatial shared component random effects and a covariate for healthy behavior. The model was applied to the joint modeling of dengue, diarrhea, and tuberculosis in thirty districts in Bandung, Indonesia over a five-year period. Our findings show that the joint model was effective in understanding the characteristics of the diseases. One potential advantage of using shared component models is that they can identify diseases with spatial or temporal distribution patterns and consider shared risk factors that may be spatially correlated, such as climate. It is recommended to conduct exploratory analyses to determine the correlation between the risks of the diseases being studied and the reference disease before using this type of model.

The main objective of spatiotemporal analysis is to offer precise predictions of outcomes. The objective of this study is to assess the accuracy of the Bayesian Latent Gaussian Model in predicting outcomes by utilizing both time-varying and fixed spatial weight matrices. The results of the Monte Carlo simulation suggest that when there is moderate spatial autocorrelation (between 0.3 and 0.7), it is strongly advised to use a time-varying spatial weight matrix. This approach yields the most precise predictions and minimizes any distortion in parameter estimates. Furthermore, we provide an illustrative case study where we simulate the effects of exposure to multiple pollutants on tuberculosis. The analysis revealed that particulate matter 10 (PM10), nitrogen oxides (NO2), sulfur dioxide (SO2), carbon monoxide (CO), and ozone (O3), have a positive influence on the risk of TB, with spatial effects that change over time. The model demonstrates that a rise of 1 mg/m³ in the levels of PM10, NO2, SO2, CO, and O3 is linked to corresponding increases in TB cases by 2.1%, 21.17%, 13.20%, 6.72%, and 6.59%, respectively. NO2 and SO2 have the most significant influence on the risk of tuberculosis (TB). These findings enhance our comprehension of the spatial correlation of TB over time and promote further investigation to determine the most efficacious strategies for mitigating the dissemination of TB.

Stock prices of different companies frequently display similar temporal fluctuations because of common influencing factors. Accurate prediction of stock prices is of utmost importance for investors in determining their investment strategies. Utilizing multivariate forecasting, which involves analyzing multiple time series, has been shown to be highly effective and efficient when applied to stocks that exhibit similar temporal patterns. It is possible to model the relationship between shares by using a shared temporal model approach. Nevertheless, it is important to note that not all stocks selected for prediction demonstrate a strong correlation; certain stocks may deviate from expected patterns. Therefore, the direct implementation of a comprehensive shared temporal component model is not universally applicable. This study presents a new method called the Semi-Shared Temporal Model, which focuses on the correlation structure among variables that have similar patterns, while also modeling all stocks simultaneously. This methodology is applied to the three leading stocks of 2023: Amazon (AMZN), Alphabet (GOOG), and MercadoLibre (MELI). Based on monthly data collected from January 2010 to December 2023, the study forecasts the stock prices for the months of January to December 2024. The analysis findings suggest that the temporal patterns of AMZN and GOOG shares are highly similar, which supports the idea of modeling them together with shared temporality. Three forecasting methods are utilized: univariate models, full shared temporal models, and semi-shared temporal models. The analysis determines that the semi-shared temporal model approach produces the most precise forecasting outcomes, with a Mean Absolute Percentage Error (MAPE) of 17.97%, surpassing both univariate and full shared temporal models. The forecast for 2024 indicates a favorable trajectory for all three stocks.

Deep learning techniques are making significant contributions to the rapid advancements in forecasting. A standout algorithm known for its ability to produce accurate forecasts by recognizing temporal autocorrelation within the data is the Long Short-Term Memory (LSTM) algorithm, a component of Recurrent Neural Networks (RNN). The LSTM method employs both stateless and stateful architecture approaches, providing versatility in its application. This research aims to compare stateful and stateless algorithms in LSTM models, focusing on forecasting stock prices, such as those of Apple Inc. This comparative analysis is crucial, taking into account various characteristics of time series data, including the benefits and drawbacks of temporal autocorrelation. The comparison results reveal that, despite the stateful algorithm requiring more computational time, it achieves greater accuracy than the stateless approach. The forecast indicates a potential upward trend in share prices for the period of January to December 2024, according to the projected outlook for Apple's stock value. However, it is essential to exercise prudence in interpreting these results, considering that share price fluctuations are influenced by a significant number of variables.

The Gaussian Markov Random Field (GMRF) is widely acknowledged for its remarkable flexibility, especially in the realm of high-resolution prediction, when compared to conventional Kriging methods. Rooted in the fundamental principles of Bayesian estimation, this methodology underscores the importance of a meticulous examination of prior and hyperprior distributions, along with their corresponding parameter values. Sensitivity analyses are crucial for evaluating the potential impact of these distributions and parameter values on prediction results. To determine the most effective values for hyperprior parameters, an iterative trial-and-error approach is commonly employed. In our research, we systematically assessed a variety of parameter values through exhaustive cross-validation. Our study is focused on optimizing hyperprior parameter values, with a particular emphasis on Penalized Complexity (PC). We applied our method to conduct spatiotemporal high-resolution predictions of PM2.5 concentrations in Jakarta province, Indonesia. Achieving accurate predictive modeling of PM2.5 concentrations in Jakarta is contingent upon this optimization. We identified that the optimal values for PC hyperprior parameters, with a range of less than 2,000 and a hyperprior standard deviation greater than 1 with a 0.1 probability, yield the most accurate predictions. These parameter values result in the minimum mean absolute percentage error (MAPE) of 19.35393, along with a deviation information criterion (DIC) of -154.23. Our findings highlight that the standard deviation parameter significantly influences model fit compared to the relatively insignificant impact of the range parameter. When coupled with high-resolution mapping, these optimized parameters facilitate a comprehensive understanding of distribution patterns. This process aids in detecting areas particularly susceptible to risks, thereby enhancing decision-making efficacy regarding air quality management.

The main objectives of this research are to identify significant spatial and temporal components associated with diarrhea and provide an accurate forecast. Using data from the Ban-dung city health surveillance system, the analysis reveals a decreasing trend in both the number of incidences and the estimated relative risks of diarrhea in most districts. Key factors contributing to diarrhea variation include temporally structured, spatially structured, and unstructured effects of space-time interaction Type I. No clear seasonal pattern is observed in diarrhea incidence among children under five, emphasizing the need for consistent vigilance and preventive measures. Spatial clustering was observed in the eastern and western parts of Bandung city. The forecasting model predicts a continued decline in diarrhea incidence and relative risk throughout 2022.