Extensões da análise discriminante em dados espaciais: simulação e aplicação em classificação de cafés

Abstract

Discriminant analysis is a widely used statistical tool for classifying observations from different populations. However, the presence of spatial dependence in the data, common in georeferenced samples of agricultural products, may compromise the performance of traditional methods. This thesis evaluates linear and quadratic discriminant analysis techniques, including sparse, robust, and spatial extensions, and proposes approaches that incorporate spatial dependence through geostatistical models, with the aim of improving the discrimination of specialty coffee quality produced in the microregions of Serra da Canastra and Serra da Mantiqueira. Monte Carlo simulation studies and an empirical application using real data were conducted, allowing the comparison of methods in terms of accuracy, precision, sensitivity, and specificity. The results indicated superior performance of models that account for spatial dependence, with emphasis on the spatial quadratic model (SPQDA), which showed a better balance between classification errors, especially in scenarios with higher spatial complexity. In addition to the methodological contribution, an interactive Shiny application was developed to facilitate the practical use of the proposed techniques, expanding access for researchers and professionals in the coffee sector. The proposed approach constitutes a robust tool for the analysis of sensory data with spatial dependence, with potential applications in other agro-environmental and georeferenced contexts.