This is a series of six half-day workshops delivered both online or in person (at UEA). This online course will help researchers develop skills to understand complex data sets by analysing data using multivariate methods. The course covers both principles and practice and focuses on Bayesian methods for model selection, regularisation and inference.
What is fMRI data? What is EEG data?
What do researchers want to find out from this data?
Includes virtual tour of the UEA Wellcome-Wolfson Brain Imaging Centre (UWWBIC) during an fMRI experiment.
An introduction to the principles of Bayesian inference and how they can be applied, using the example of Linear Regression - where you have multiple independent variables (‘inputs’) and one dependent variable (‘output’).
Bayesian Foundations & Basic Linear Models
Demo 1 - Bayesian One-Way ANOVA: Gaussian and T Methods
Demo 2 - Bayesian One-Way ANOVA: Simulation and Method Comparison
Demo 3 - Bayesian One-Way ANOVA: GLM Approach with Confounds
Demo 4 - General Linear Model: Hypothesis Testing with Contrasts
Advanced Bayesian Linear Models and Robustness
Demo 5 - Robust GLM: Parameter Estimation with Gaussian Mixture Noise
Model Comparison and Bayes Factors
Demo 6 - Bayes Factors: Comparing Savage-Dickey vs Two-Model
Demo 7 - Bayes Factors: Comparing Estimation Methods: Savage-Dickey, MultiFit, and Default
Bayesian Hypothesis Testing: One-Sample t-Tests
Demo 8 - One-Sample t-Test: Bayes Factors on Arbitrary Scales
Demo 9 - One-Sample t-Test: Bayes Factors on Standard Scales
Where you have multiple independent variables (‘inputs’) and multiple dependent variables (‘outputs’)
e.g. multiple behavioural variables, and multiple brain activation variables. This workhorse is the basis of Multivariate ANOVAs and neural “encoding” methods (that map from behaviour to brain).
Multivariate Linear Regression
Demo 1 - MLM: Basic Bayesian MLM Estimation
Demo 2 - MLM: Post-hoc Hypothesis Testing (Savage-Dickey)
Demo 3 - MLM: Comparing Shrinkage Priors
Demo 4 - Multivariate t-Distribution: Using Normal-Wishart Conjugate Prior
Demo 5- Comparing Multivariate Models: Canonical Correlation Analysis (CCA) vs MLM
Linear Mixed Effects
Demo 6 - Bayesian Linear Mixed Effects Modelling: Hierarchical Parameter Estimation and Shrinkage
Autoregression
Demo 7 - AR Modelling: Estimating AR Parameters from Simulated AR-5 Process
Demo 8 - Multivariate AR (MAR): Estimating MAR Parameters from Simulated Bivariate Time Series
Demo 9 - Robust AR (RAR): Detecting Outliers in AR Processes with Heavy-Tailed Noise
Spectral analysis
Demo 10 - Spectral Analysis: Estimating Power Spectrum Using AR Models
Demo 11 - Spectral Analysis: Estimating Granger Causality in the Frequency Domain Using Bivariate MAR Models
Demo 12 - Spectral Analysis: Granger Causality for Multivariate Time Series Using MAR Models
Demo 13 - Spectral Analysis: MAR Spectral Estimation with Multidirectional Coupling
Demo 14 - Spectral Analysis : Partial Directed Coherence (PDC) and Directed Transfer Function (DTF)
Demo 15 - Spectral Analysis: Time-Frequency Analysis Using Wavelets
Includes Bayesian Logistic Regression, Softmax Regression, Naïve Bayes and Support Vector Machines. These form the basis of neural “decoding” methods, that map from brain to behaviour.
This session will also cover Representational Similarity Analysis (RSA; where we look for similarities between e.g. correlations among neural representations and correlations in behaviour).
Logistic Regression
Demo 1 - Logistic Regression: Two-Class 2D Data
Demo 2 - Logistic Regression: Using Example Ionosphere Dataset
Softmax Regression
Demo 3 - Softmax Regression: Two-Class 2D Data
Demo 4 - Softmax Regression: Three-Class 2D Data
Support Vector Machines
Demo 5 - SVM: SVM Classification of Example Datasets
Includes Bayesian Canonical Variates Analysis (CVA) and Partial Least Squares (PLS).
These methods can identify “modes of variation” that identify multivariate mappings, for example, between brain and behaviour.
Principal Component Analysis
Demo 1 - Bayesian PCA: Estimating the Number of Latent Sources
Demo 2 - Singular Value Decomposition (SVD): Image Compression and Dimensionality Reduction
Demo 3 - Variational PCA : Dimensionality Reduction
Demo 4 - Variational PCA: Model Comparison and Covariance Estimation
Canonical Variates Analysis (CVA) / Canonical Correlation Analysis (CCA)
Demo 5 - CVA: Bayesian Model Order Selection
Demo 6 - CVA: Estimating Canonical Vectors For a Fixed Model Order
Demo 7 - CCA: Estimating Factor Matrices From Data With Shared Latent Variables
Demo 8 - CCA: Analysis of Independent Data Sources
Includes Mixtures of CVAs, Mixtures of Gaussians and Neural Networks (Multilayer Perceptrons).
Some encoding/decoding problems can only be addressed using nonlinear methods.
Mixture Canonical Correlation Analysis (MCCA)
Demo 1 - MCCA: Estimating Factor Matrices From Data With Shared Latent Variables
Demo 2 - MCCA: Predicting Latent Variables From Multiple Data Views
Demo 3 - MCCA: Identifying the Number of Clusters Using Model Evidence
Mixtures of Gaussians
Demo 4 - Gaussian Mixture Model (GMM): Incremental GMM learning on 2D Clustered Data
Demo 5 - Gaussian Mixture Model (GMM): Variational Bayesian GMM on 1D Data
Demo 6 - Gaussian Mixture Model (GMM): Variational Bayesian GMM on 2D Data with Fixed Number of Components
Non-linear Components
Demo 7 - Nonlinear Component Analysis (NCA): Bayesian Regularisation for Dimensionality Reduction
Demo 8 - Nonlinear Component Analysis (NCA): Feature Selection Using Bayesian Pruning