resources

Below is a list of overloaded theoretical/experimental resources:

• Overloaded probability density functions in Bayesian statistics

  • usual probability density functions (exponential family) (wikipedia)

  • transformation of variables (www.math.uah.edu)

  • analytic approximations (and bounds) to the marginal likelihood in Bayesian inference (personal notes)

  • a semi-analytical approximation to the expected log-transformed Beta variable for small shape parameters (personal notes)

  • notes on the relatives entropies of Gaussian and Gamma probability density functions (personal notes)

• Linear algebra for statistics

  • a matrix oriented note on joint, marginal, and conditional multivariate Gaussian distributions (Newman & Leonard)

  • the matrix cookbook (Petersen & Pedersen)

  • notes on matrix calculus (www4.ncsu.edu/~pfackler/)

  • old and new matrix algebra useful for statistics (Minka)

  • Kronecker product (Schäcke) and the Vec operator (Scott)

• On Variational Bayesian Analysis

  • elements of variational calculus (S. Jbabdi thesis)

  • variational Free Energy and the Laplace approximation (Friston)

  • notes on the model evidence of a GLM at the frequentist limit (personal notes)

  • VB treatment of the mixture of Gaussian (MoG) model (personal notes)

  • notes on Dirichlet processes (personal notes)

  • notes on the lagged Kalman update on nonlinear stochastic dynamical systems (personal notes)

  • notes on group-level Bayesian model comparison (personal notes)

  • notes on the VB treatment of mixed-effects models (personal notes)

  • notes on parameter transformations for emulating sparse priors (personal notes)

  • notes on VBA's modified Gauss-Newton optimization scheme (personal notes)

  • VB for generative models with un-normalized likelihoods (personal notes)

  • VB and the Fokker-Planck equation (personal notes)

• On learning and/or decision models

  • • derivation of a Bayesian model of attitude alignment (personal notes)

    • derivation of the "influence learning" model from Hampton et al. (2007) (personal notes)

    • on the numerical stability of the early-stopping Gauss-Newton rule in HGF-like models (personal notes)

    • modelling counterfactual reasoning in learning tasks (personal notes, unfinished)

    • modelling the influence of false feedback on perceptual learning (personal notes, unfinished)

    • dynamical analysis of RL learning models (personal notes, unfinished)

    • factorial Bayesian modelling for operant learning within an unstable environment: heuristics, counterfactuals and exploration (personal notes, unfisnished)

    • a note on diffusion/drift and related race models (personal notes)

    • modelling cognitive dissonance under the FEP (personal notes, unfinished)

    • revisiting the prisoner's dilemma (personal notes)

• Dynamical systems

  • notes on dynamical systems: integral/differential forms, Lyapunov exponents, … (personal notes)

  • notes on the continuous limit in statistical mechanics (www.nyu.edu/classes/tuckerman/)

  • reinterpreting effective connectivity using causal calculus (personal notes)

  • master equation and Fokker-Planck formalism (Aslangul)

• EEG/MEG/fMRI

  • guidelines for Standard Electrode Position Nomenclature (American Clinical Neurophysiology Society)

  • the five percent electrode system for high-resolution EEG and ERP measurements (Oosteneld & Praamstra)

  • visual evoked potentials standard (Odom et al.)

  • practical fMRI: the nuts and bolts (www.practicalfmri.blogspot.co.uk)