Statistical Models of the Brain

Statistical Models of the Brain is a course in computational neuroscience I began teaching in 2011. Brent Doiron co-taught it with me on 4 occasions, 2016-2019. It has evolved a lot, mainly in terms of refined focus and pedagogy.

A quick video summary (less than 5 minutes) of the Spring 2021 version may be found here: Wrap up

In 2021 I decided to create short video lectures, 15-30 minutes, that students would view prior to class. Topics with links are listed below.

For additional details see the web page on Statistical Models of the Brain.

Topics

• 1. What is computational neuroscience?
• 2. (Background) Random variables; What is a statistical model? Fitting statistical models to data.
• 3. (Background) Statistical independence of random variables; log transformations
  
• 4. (Background) The Law of Large Numbers and the Central Limit Theorem; statistical estimation; least-squares linear regression and the linear algebra concept of a basis.
  
• 5a. Random walk integrate-and-fire models and balanced excitation and inhibition
• 5b. Extra Point Processes
• 6a. Population vectors
• 6b. BCI
• 7. Information theory in human discrimination
• 8. (Background) Differential equations
• 9. Electrical circuit model of a neuron; passive synaptic dynamics and phenomenological models of spiking; integrate-and-fire dynamics
• 10. The Hodgkin-Huxley model of action potential generation (Nour Riman)
• 11. Network dynamics (No Video)
• 12. (Background) Bayes' Theorem; optimality of Bayesian classifiers; mean squared error; Bayes and maximum likelihood.
• 13. Cognition and optimality; ACT-R
• 14. (Background) Statistical tests, ROC curves, signal detection theory
• 15. Optimal observers in perception and action
• 16. (Background) Regression and generalized regression.
• 17. Firing rate and neural coding; spike trains as point processes
• 18. Information theory in neural coding (2nd video)
• 19. Neural implementation of Bayesian inference
• 20. Population-wide variability: spike count correlations; dimensionality reduction
• 21. Neural basis of decision making (systems level)
• 22. Network models of working memory and decision-making (Chencheng Huang)
• 23. Oscillations and coordinated neural activity.
• 24. Reinforcement learning
• 25. Graphs and networks
• 26. What is science? (Additional video: wrap-up)

Other Videos for Teaching and Training

• Bayes Theorem and Bayesian Inference (12.5 minutes)
• Beautiful Formulas, and a beautiful Bayesian formula (21 minutes)