William Marshall

Professor, Mathematics & Statistics

BSc (Brock), MMath, PhD (Waterloo)
Office: Mackenzie Chown J403
905 688 5550 x3940

My primary research interest is computational statistics with applications to neuroscience. My current work falls into three main categories:

  • Causal Networks – The brain can be viewed abstractly as a complex network of interacting elements (whether as neurons, mini-columns, etc.). This aspect of my research focuses on developing and exploring information theoretic and causal measures of complexity (e.g., integrated information) to apply to causal/Bayesian networks. I’m specifically interested in measures which can be applied across spatiotemporal scales.
  • Measures of connectivity – Neuroimaging methods (e.g., electroencephalography, functional magnetic resonance imaging, calcium imaging) generate large amounts of data. I am interested in developing measures of functional connectivity between recording areas (brain regions). To do this, I utilize signal processing techniques and statistical learning methods. Developing such methods requires substantial domain specific knowledge of the imaging modality. This aspect of my research can be viewed as an empirical analogue of (A).
  • Linear Mixed Effect (LME) Models – The nature of neuroscience experiments is such that there are often several measurements taken from a single experimental unit (e.g., multiple synapses from a single dendrite and multiple dendrites from a single mouse). Linear mixed effect models are a powerful and flexible tool for such “repeated measures” experiment designs. This aspect of my research aims to develop model fitting and inference methods for LME models, with specific thought to neuroscience experiments.

Recent Publications

Spano, G., Banningh, S., Marshall, W., de Vivo, L., Bellesi, M., Loschky, S., Tononi, G., Cirelli, C. (2019) Short sleep deprivation increases synapse density and axon-spine interface in the hippocampal CA1 region of adolescent mice. Journal of Neuroscience, 0380-19.

Nilsen, A., Juel, B., Marshall, W. (2019) Evaluating Approximations and Heuristic Measures of Integrated Information. Entropy, 21(5), 535.

Albantakis, L., Marshall, W., Hoel, E.P., Tononi, G. (2019) What caused what? A Quantitative Account of Actual Causation Using Dynamical Causal Networks. Entropy, 21(5), 459.

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).

Bourdon, A.K., Spano, G., Marshall, W., Bellesi, M., Tononi, G., Serra, P.A., Baghdoyan, H.A., Lydic, R., Campagna, S.R., Cirelli, C. (2018) Metabolomic analysis of mouse prefrontal cortex reveals upregulated analytes during wakefulness compared to sleep. Scientific Reports, 8(1).

Mensen, A., Marshall, W., Saisai, S., Tononi, G. (2018) Differentiation Analysis of Continuous EEG Activity Triggered by Video-clip Contents. Journal of Cognitive Neuroscience, 30(8).

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

Bellesi, M., Haswell, D., de Vivo, L., Marshall, W., Tononi, G., Cirelli, C. (2018) Myelin modifications after chronic sleep loss in adolescent mice. Sleep, zsy034.

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.

Mensen, A., Marshall, W., Tononi, G., EEG differentiation analysis and stimulus set meaningfulness. (2017) Frontiers in Psychology, 8:1748.

Funk, C., Peelman, K., Bellesi, M., Marshall, W., Cirelli, C., Tononi, G. (2017) Role of somatostatin-positive cortical interneurons in the generation of sleep slow waves. Journal of Neuroscience, 37 (38) 9132-9148.

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.

Current Teaching (2019-2020)

  • MATH5P85 – Mathematical Statistical Inference (Fall)
  • MATH3P85 – Mathematical Statistics II (Winter)
  • MATH5P87 – Computational Statistics (Winter)