PhD Defense Jacob Østergaard

Title: Statistical Methods for Neural Data Cointegration Analysis of Coupled Neurons & Generalized Linear Models for Spike Train Data

Abstract
Some of the most captivating questions in the history of science concerns the functions of the human brain and the subject has attracted researchers and philosophers for centuries. Recent advances in laboratory technology has enabled us to look further into the internal microscopic components of the brain than ever before. Neuroscience, as a purely scientific discipline, is relatively new compared to it's basic components of mathematics, physics, chemistry, and physiology. However, the current rate of experimental discoveries in neuroscience calls for new advances in analytical tools to better understand the biological processes that occur in the brain.

This thesis aims to explore new statistical models for neural data and their usefulness in analyzing experimental data. The thesis consist of two parts, one that concerns neural networks and how these can be interpreted as a cointegrated system and one that examines how the class of Generalized Linear Models can be used to decode specific behaviors of simulated neurons. Part one introduces the concept of cointegration and demonstrates how a network can be analyzed by interpreting the system as a cointegrated process. This work is then extended from a small 3-dimensional system to a high-dimensional setting and includes a discussion of future possibilities for network analysis using these techniques. Part two opens with a demonstration of how Generalized Linear Models can be designed for spike train data and how varying patterns of different neurons are captured by this class of statistical models. Part two then continues with a specialized model aimed at capturing a specific type of behavior known as "bursting”.

In the age of big data and artificial intelligence, two major themes related to neuroscience present themselves. The first is how to cope with the rapidly increasing data collection from laboratory experiments and (very) high-dimensional interacting systems. This occurs partially due to an increased interest in neuroscience, as well as the introduction of new measuring equipment. The second is the motivation for a continuously deeper understandning of the human brain. There are still countless unanswered questions regarding this biological mechanism. In order to further understand causes of neural diseases as well as continued development of artificial intelligence, these questions are important to study. Ultimately, they should lead us to a better intuition regarding the question: "how does intelligence work”?

Supervisor
Susanne Ditlevsen, MATH, University of Copenhagen

Anders Rahbek, ECON, University of Copenhagen

Assessment Committee

Niels Richard Hansen (Chair), MATH, University of Copenhagen

Rainer Dahlhaus, Universität Heidelberg

Vincent Rivoirard, Université Paris Dauphine