Banca de DEFESA: Saulo Henrique Furtado Leite

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
STUDENT : Saulo Henrique Furtado Leite
DATE: 06/10/2023
TIME: 14:15
LOCAL: PPGMAT
TITLE:

The Fisher-Rao Metric: Geometric Approach in Probability and Statistics

KEY WORDS:

Fisher Information Matrix, Riemannian Metric, Riemannian Statistical Manifold, Fisher-Rao
Distance, Kullback-Leibler Divergence, Statistical Inference.

PAGES: 113
BIG AREA: Ciências Exatas e da Terra
AREA: Matemática
SUMMARY:

 In this dissertation, we will see how the Fisher information matrix gives rise to a Riemanian metric
in regular parametric statistical models and how the concept of Riemanian statistical manifold is derived from this. We
will see that this metric provides a measure of dissimilarity between probability distributions, known as the Fisher-Rao
distance. We will show that the parametric family of multivariate Gaussian distributions is a Riemanian statistical
manifold. We will present a relationship between the Fisher-Rao distance and the Kullback-Leibler divergence. Finally,
we will illustrate through examples how tools from Riemannian Geometry can be used in questions related to
Statistical Inference.

COMMITTEE MEMBERS:
Externo à Instituição - ROBERTO IMBUZEIRO MORAES FELINTO DE OLIVEIRA - IMPA
Presidente - 1508667 - ARY VASCONCELOS MEDINO
Interna - 1522311 - DANIELE DA SILVA BARATELA MARTINS NETO
Interno - 3101411 - TARCISIO CASTRO SILVA