A Bayesian model for predicting monthly fire frequency in Kenya.

This study presents a comprehensive analysis of historical fire and climatic data to estimate the monthly frequency of vegetation fires in Kenya. This work introduces a statistical model that captures the behavior of fire count data, incorporating temporal explanatory factors and emphasizing the predictive significance of maximum temperature and rainfall. By employing Bayesian approaches, the paper integrates literature information, simulation studies, and real-world data to enhance model performance and generate more precise prediction intervals that encompass actual fire counts. To forecast monthly fire occurrences aggregated from the Moderate Resolution Imaging Spectroradiometer (MODIS) data in Kenya (2000-2018), the study utilizes maximum temperature and rainfall values derived from global GeoTiff (.tif) files sourced from the WorldClim database. The evaluation of the widely used Negative Binomial (NB) model and the proposed Bayesian Negative Binomial (BNB) model reveals the superiority of the latter in accounting for seasonal patterns and long-term trends. The simulation results demonstrate that the BNB model outperforms the NB model in terms of Root Mean Square Error (RMSE), and Mean Absolute Scaled Error (MASE) on both training and testing datasets. Furthermore, when applied to real data, the Bayesian Negative Binomial model exhibits better performance on the test dataset, showcasing lower RMSE (163.22 vs. 166.67), lower MASE (1.12 vs. 1.15), and reduced bias (-2.52% vs. -2.62%) compared to the NB model. The Bayesian model also offers prediction intervals that closely align with actual predictions, indicating its flexibility in forecasting the frequency of monthly fires. These findings underscore the importance of leveraging past data to forecast the future behavior of the fire regime, thus providing valuable insights for fire control strategies in Kenya. By integrating climatic factors and employing Bayesian modeling techniques, the study contributes to the understanding and prediction of vegetation fires, ultimately supporting proactive measures in mitigating their impact.

Assessing predictive performance of supervised machine learning algorithms for a diamond pricing model.

This study conducted a comprehensive analysis of multiple supervised machine learning models, regressors and classifiers, to accurately predict diamond prices. Diamond pricing is a complex task due to the non-linear relationships between key features such as carat, cut, clarity, table, and depth. The analysis aimed to develop an accurate predictive model by utilizing both regression and classification approaches. To preprocess the data, the study employed various techniques. The work addressed outliers, standardized the predictors, performed median imputation of missing values, and resolved multicollinearity issues. Equal-width binning on the cut variable was performed to handle class imbalance. Correlation-based feature selection was utilized to eliminate highly correlated variables, ensuring that only relevant features were included in the models. Outliers were handled using the inter-quartile range method, and numerical features were normalized through standardization. Missing values in numerical features were imputed using the median, preserving the integrity of the dataset. Among the models evaluated, the RF regressor exhibited exceptional performance. It achieved the lowest root mean squared error (RMSE) of 523.50, indicating superior accuracy compared to the other models. The RF regressor also obtained a high R-squared ([Formula: see text]) score of 0.985, suggesting it explained a significant portion of the variance in diamond prices. Furthermore, the area under the curve with RF classifier for the test set was 1.00 [Formula: see text], indicating perfect classification performance. These results solidify the RF's position as the best-performing model in terms of accuracy and predictive power, both in regression and classification. The MLP regressor showed promising results with an RMSE of 563.74 and an [Formula: see text] score of 0.980, demonstrating its ability to capture the complex relationships in the data. Although it achieved slightly higher errors than the RF regressor, further analysis is needed to determine its suitability and potential advantages compared to the RF regressor. The XGBoost Regressor achieved an RMSE of 612.88 and an [Formula: see text] score of 0.972, indicating its effectiveness in predicting diamond prices but with slightly higher errors compared to the RF regressor. The Boosted Decision Tree Regressor had an RMSE of 711.31 and an [Formula: see text] score of 0.968, demonstrating its ability to capture some of the underlying patterns but with higher errors than the RF and XGBoost models. In contrast, the KNN regressor yielded a higher RMSE of 1346.65 and a lower [Formula: see text] score of 0.887, indicating its inferior performance in accurately predicting diamond prices compared to the other models. Similarly, the Linear Regression model performed similarly to the KNN regressor, with an RMSE of 1395.41 and an [Formula: see text] score of 0.876. The Support Vector Regression model showed the highest RMSE of 3044.49 and the lowest [Formula: see text] score of 0.421, indicating its limited effectiveness in capturing the complex relationships in the data. Overall, the study demonstrates that the RF outperforms the other models in terms of accuracy and predictive power, as evidenced by its lowest RMSE, highest [Formula: see text] score, and perfect classification performance. This highlights its suitability for accurately predicting diamond prices. The study not only provides an effective tool for the diamond industry but also emphasizes the importance of considering both regression and classification approaches in developing accurate predictive models. The findings contribute valuable insights for pricing strategies, market trends, and decision-making processes in the diamond industry and related fields.

Application of optimal control to the onchocerciasis transmission model with treatment.

In this paper, we present a model for onchocerciasis that considers mass administration of ivermectin, contact prevention controls and vector elimination. The model equilibria are computed and stability analysis carried out in terms of the basic reproduction number R0. The model is found to exhibit a backward bifurcation so that for R0 less than unity is not sufficient to eradicate the disease from the population and the need is to lower R0 to below a certain threshold, R0c for effective disease control. The model is fitted to data on individuals with onchocerciasis in Ghana. A sensitivity analysis reveals that the parameters with the most control over the epidemic are the vector death rate and the effective contact rates between susceptible individuals and infected vector and susceptible vector with infected individuals. This suggests that programs aimed controlling vector will be significantly more effective in combating the disease. Optimal control theory is applied to investigate optimal control strategies for controlling onchocerciasis using insect repellent and both insecticide and larvicide as system control variables. We use Pontryagin's Maximum Principle to show the necessary conditions for the optimal control of onchocerciasis. Numerical simulations of the model show that restricted and proper use of control measures might considerably decrease the number of infections in the human population.