This lecture course was given in the Spring Term of 2013 at the Wellcome Trust Centre for Human Neuroimaging at UCL. It explains the principles of Bayesian inference showing how they are used in neuroimaging. Each lecture is 1 hour long and there are worksheets and matlab code to play with. You'll need SPM on your matlab search path to run the code.
- Bayes rule, Medical Decision Making, Odds Ratios, Generative Models, Marginalisation, Explaining Away.
PDF
- Bayes Rule for Gaussians, Perception as Statistical Inference, Sensory Integration, Flanker task, Conflict detection. PDF
- Maximum Likelihood, fMRI analysis, Bayesian GLMs, Augmented Form, MEG Source Reconstruction. PDF More detailed notes on Bayesian MEG: PDF.
- Bayes rule for models, Bayes factors, Model Evidence, Accuracy and Complexity, AIC and BIC, Linear model example, Multilayer Perceptron, Laplace Approximation, Cross Validation. PDF
- Linear models with (i) isotropic covariances, (ii) linear covariances. Global Shrinkage priors. MEG source reconstruction. Sparse Coding, Receptive Fields, Nonlinear Inhibition. PDF
- Information, Entropy, Kullback Liebler Divergence, Asymmetry, Free Energy, Factorised Approximations. PDF
- Variational Laplace algorithm, priors, energies, adaptive step size, approach to limit example, Fitzhugh-Nagumo example, Metropolis-Hastings. PDF
Worksheets and Matlab Code
- Worksheet 1: WORD
- Worksheet 2: WORD
- Matlab Code Archive: ZIP