Randomized confidence and credibility intervals for point processes.

• Grant number: 25/06016-3
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: August 01, 2025
• End date: February 28, 2029
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Applied Probability and Statistics
• Principal Investigator: Nancy Lopes Garcia
• Grantee: Carlos Henrique Trigo Nasser Felix
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 23/13453-5 - Stochastic systems modeling, AP.TEM

Abstract

During the masters degree, the candidate developed a fuzzy confidence intervalmethod based on the Neyman-Pearson lemma of simple hypotheses in such a waythat it is defined for any parametric family of distributions and has a smaller expectedsize at a specific value compared to any other method. Furthermore, it was possible todetermine a lower limit for the expected size of the interval. Motivated by these results,this project intends to extend the developed methodology, through the construction ofrandomized confidence intervals for the parameters of interest of point processes thatare absolutely continuous with respect to the homogeneous Poisson process with arate equal to 1. Furthermore, it is intended to use the Bayesian paradigm to incorporatea prior information and construct credibility intervals also under the fuzzy theory. Thetheoretical development of the methodology is planned in addition to its computationalimplementation, with the construction of a statistical package. (AU)