Método de segmentação por boxplot circular para dados multimodais e sua aplicação na análise de captura de enxames de abelhas com eventos recorrentes

Abstract

Circular statistics is applied across various scientific fields, particularly when data involve seasonality, time, or directions. Multimodality in datasets poses a significant challenge for statistical analysis and modeling, a common issue in circular data where modal subsets are often segmented empirically, such as by days of the week or seasons. Alternatively, maximization algorithms based on mixtures of von Mises distributions are used, requiring advanced theoretical knowledge. This thesis, structured in four articles, proposes innovative approaches to address these challenges. The first article introduces a segmentation method based on the construction of a circular boxplot, with its effectiveness validated through simulations across diverse scenarios and applied to multimodal traffic accident timing data throughout the week, demonstrating a balance between simplicity and accuracy. The second article extends this methodology, refining the circular boxplot approach for enhanced precision in multimodal data analysis. The third article presents an experiment characterizing Africanized bee swarm capture over one year using trap nests, recording linear variables (height, altitude, precipitation, humidity, wind speed) and circular variables (wind direction, capture season, longitude, latitude, nest entrance angle relative to magnetic North), alongside the qualitative variable of trap nest coating color. Bimodal patterns in capture seasons were analyzed using the circular boxplot segmentation method developed in the first article, with relationships between variables explored through linear-linear, linear-circular, and circular-circular correlations based on their nature. The fourth article addresses censored data, as capture dates were recorded within intervals between the last day without a swarm and the observation day, employing survival analysis with the Andersen-Gill model, incorporating linear and circular covariates to model swarm capture time, with bimodal segmentation via circular boxplot. Additionally, two seasonal periods—post-rain (April 10 to June 6) and pre-rain (August 29 to October 19)—were segmented to account for the bimodal patterns observed in swarm capture characterization. The proposed methods and findings offer practical and accessible tools for analyzing multimodal circular data, with applications in traffic safety and beekeeping, supporting biodiversity and food security through enhanced swarm capture efficiency.