Inference for non-Poissonian point processes

• Grant number: 16/09390-4
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: September 01, 2016
• End date: April 12, 2018
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal Investigator: Nancy Lopes Garcia
• Grantee: Guilherme Vieira Nunes Ludwig
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

Poisson processes are one of the most popular point process models for count data. Many natural phenomena can be described with this process, and estimation of parameters is usually easy. The basic assumption for a spatial Poisson process is independence between disjoint sets. However, data from many applications show interaction between points, either by clustering or repulsion. In this project proposal we will work on two problems: (1) What happens in regression analysis for point processes when we use the likelihood function for a Poisson process, while the underlying (true) process is non-Poissonian? We know that coefficient estimates are consistent, but can the estimates be made more efficient by employing a semi-parametric model? (2) How can we obtain estimates for point processes with repulsion using Papangelou densities with respect to Poisson process?

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

GARCIA, NANCY L.; GUTTORP, PETER; LUDWIG, GUILHERME. Interacting cluster point process model for epidermal nerve fibers. SPATIAL STATISTICS, v. 35, MAR 2020. (14/26419-0, 16/09390-4, 18/09877-6, 17/15306-9)