High Dimensional Statistical Inference for Stochastic Processes with application in Neuroscience

• Grant number: 18/25076-3
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: April 01, 2019
• End date: July 31, 2019
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Probability
• Principal Investigator: Florencia Graciela Leonardi
• Grantee: Ricardo Felipe Ferreira
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 13/07699-0 - Research, Innovation and Dissemination Center for Neuromathematics - NeuroMat, AP.CEPID

Abstract

Over the past years, with the computational advances, statistics have undergone drastic changes, especially with regard to the increasing capacity of data storage. For each individual, more and more features have been collected, then the number of parameters to be estimated have becomes much larger than the number of observations. It is the case, for example, of areas as biology or applications where each observation consists of an image or a text document, complex objects which requires more elaborated statistical methods.Neuronal activity is manifested by emission, along the time, of spike trains generated by excitations coming from other neurons or external sources. In this sense, the neuronal dynamic can be described by an auto-regressive stochastic process taking values on a suitable configuration space. While neuronal activity can be directly observed, the interactions among neuronal structures can only be inferred from data. However, there are millions of neurons in each component of neural circuit and we have access just to a small part of it. Since we are interested in a framework where the number of observed spikesis much larger than number of neurons within study, the inference of functional interaction among these components is performed in a high-dimensional environment.Therefore, the main goals of this research project are: (1) to extend the results obtained in candidate's phd thesis, i.e., to generalize estimation proprieties of the information flowing between two neuronal spike trains for the case where the number of neurons is n > 2; (2) to propose a methodology of high dimensional statistical inference for stochastic process and (3) to analyze the practical efficiency of the results obtained using real data.