Bayesian Inference Course
This short lecture course will describe the principles of Bayesian inference and show how it is used in neuroimaging. Lectures will be midday on Thursdays starting 31 Jan 2013. They will take place in the FIL Seminar Room, 12 Queen Square. Click here for directions.
Each lecture is 1 hour long and there are worksheets and code to play with. You'll need SPM on your matlab search path to run the code.
The lecture slides below are from a previous course I ran at Virginia tech. I will use these slides and update them as we go along. The last slide in each talk gives a list of papers on which the talk is based.
All welcome. Any queries, send me an email (w.penny AT ucl).
Introduction Bayes rule, Medical Decision Making, Odds Ratios, Generative Models, Marginalisation, Explaining Away. 31 Jan 2013.
The Bayesian Brain Bayes Rule for Gaussians, Perception as Statistical Inference, Sensory Integration, Flanker task, Conflict detection. 7 Feb 2013
(Code: flanker_demo.m)
Linear Models Maximum Likelihood, fMRI analysis, Bayesian GLMs, Augmented Form, MEG Source Reconstruction. (More detailed notes on Bayesian MEG ) 14 Feb 2013.
Model Comparison Bayes rule for models, Bayes factors, Model Evidence, Accuracy and Complexity, AIC and BIC, Linear model example, Multilayer Perceptron, Laplace Approximation, Cross Validation. 21 Feb 2013
Empirical Bayes Linear models with (i) isotropic covariances, (ii) linear covariances. Global Shrinkage priors. MEG source reconstruction. Sparse Coding, Receptive Fields, Nonlinear Inhibition. 28 Feb 2013
Variational Inference Information, Entropy, Kullback Liebler Divergence, Asymmetry, Free Energy, Factorised Approximations. 7 Mar 2013.
Nonlinear Models Variational Laplace algorithm, priors, energies, adaptive step size, approach to limit example, Fitzhugh-Nagumo example, Metropolis-Hastings. 14 Mar 2013.
Worksheet 1
Worksheet 2
Matlab Code Archive