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"?