My primary research interest is computational statistics with applications to neuroscience. My work centers on developing statistical and information-theoretic methods for understanding complex neural systems and, more recently, exploring their implications for artificial agents.

(A) Causal Networks.

I study the brain as a complex network of interacting elements—from neurons to mesoscopic circuits to large-scale regions. This line of research develops and analyzes information-theoretic and causal measures of network structure and complexity, such as integrated information, with an emphasis on measures that apply robustly across spatial and temporal scales.

(B) Measures of Connectivity in Neuroimaging.

Neuroimaging modalities such as EEG, fMRI, and calcium imaging generate large, noisy, and high-dimensional datasets. I develop methods for assessing functional connectivity between brain regions by combining signal processing, statistical learning, and modality-specific domain knowledge. This work provides empirical counterparts to my theoretical research on causal structure.

(C) Integrated Information Theory and Artificial Consciousness.

I investigate statistical and computational aspects of integrated information theory (IIT), with a particular focus on how measures of causation and complexity may help explain how consciousness arises from physical systems.

(D) Sports Analytics (Secondary Area).

As a secondary research direction, I apply statistical modeling and machine learning to problems in sports analytics, including player evaluation, forecasting, and strategy quantification. This work provides a complementary applied setting for developing and testing statistical methods.

Findlay, G., Marshall, W., Albantakis, L., David, I., Mayner, W. G., Koch, C., & Tononi, G. (2024). Dissociating artificial intelligence from artificial consciousness. arXiv preprint arXiv:2412.04571.

Albantakis, L., Barbosa, L., Findlay, G., Grasso, M., Haun, A. M., Marshall, W., … & Tononi, G. (2023). Integrated information theory (IIT) 4.0: Formulating the properties of phenomenal existence in physical terms. PLoS computational biology, 19(10), e1011465.

Miyamoto, D., Marshall, W., Tononi, G., & Cirelli, C. (2021). Net decrease in spine-surface GluA1-containing AMPA receptors after post-learning sleep in the adult mouse cortex. Nature communications, 12(1), 2881.

Barbosa, L. S., Marshall, W., Streipert, S., Albantakis, L., & Tononi, G. (2020). A measure for intrinsic information. Scientific reports, 10(1), 18803.

Mayner, W.G.P, Marshall, W., Albantakis, L., Findlay, G., Marchman, R., Tononi, G. (2018) PyPhi: A toolbox for integrated information theory. PLoS Comput Biol, 14(7).

Marshall, W., Albantakis, L., Tononi, G. (2018) Blackboxing and cause-effect power. PLoS Comput Biol, 14(4).

Marshall, W., Kim, H., Walker, S.I., Tononi, G., Albantakis, L. (2017) How causal analysis can reveal autonomy in models of biological systems. Philosophical Transactions of the Royal Society: A, 375:20160358.

de Vivo, L., Bellesi, M., Marshall, W., Bushong, E., Ellisman, M., Tononi, G., Cirelli, C. (2017) Ultrastructural evidence for synaptic scaling across the wake/sleep cycle. Science, 355(6324), 507-510.

Winter 2026

• STAT3P87 – Statistical Computing with R

Winter 2025

• STAT4P82/5P82 – Nonparametric Statistics
• STAT5P87 – Computational Statistics

Fall 2024

• STAT3P82 – Regression Analysis