Methodological Research and Statisitical Modelling in Neuroscience

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The brain is, arguably, the most sophisticated organ in the human body. With approximately 100 billion nerve cells (a.k.a. neurons), each potentially connected (through synapses) to thousands of other neurons, the brain is a complex network of interconnected cells. These cells communicate through sequences of electrochemical waves, which are called spike trains. This research proposal focuses on multivariate, multiscale, and Bayesian extensions of state-of-the-art models in statistical modelling of neural spike trains. Recent data acquisition developments allow experimentalists to simultaneously record the electrical activity of several hundreds of neurons. This highlights the need for efficient data visualization methods, and multivariate statistical theories tailored for neural spike trains. Following my main research interests, i.e. computational neuroscience, this proposal focuses on four areas unified by the ultimate goal of understanding information coding processes in the brain. In particular, 1) we will develop a multivariate point process framework (multivariate Skellam Process with Resetting) for the analysis of multiple neural spike trains, which is both biologically justifiable and computationally efficient. 2) Within the multivariate point process framework developed in (1), we will develop models to capture over and under dispersed spiking activity (relative to Poisson) observed in real data. Since under-dispersed models for neural spike trains are rare and not well-studied in the literature, the outlined research will be impactful to the discipline. 3) We will develop multiscale multivariate models to capture neural spiking patterns from multiple time scales. Such patterns are frequently observed (simultaneously) in real data across different brain regions, and developing statistical models to study such data are necessary. 4) We will develop Bayesian extensions of the methods proposed in the previous three research activities. The above-mentioned research activities will build on and extend my previous work on the analysis of neural spike trains, and provide excellent opportunities for undergraduate, masters, and doctoral level training in this cutting-edge multidisciplinary research area.