Co-Planar Stereotaxic Atlas of the Human Brain—3-Dimensional Proportional System: An Approach to Cerebral Imaging, J. Talairach, P. Tournoux. Georg Thieme Verlag, New York (1988), 122 pp., 130 figs. DM 268

Statistics for Spatial Data.

A free-energy principle has been proposed recently that accounts for action, perception and learning. This Review looks at some key brain theories in the biological (for example, neural Darwinism) and physical (for example, information theory and optimal control theory) sciences from the free-energy perspective. Crucially, one key theme runs through each of these theories — optimization. Furthermore, if we look closely at what is optimized, the same quantity keeps emerging, namely value (expected reward, expected utility) or its complement, surprise (prediction error, expected cost). This is the quantity that is optimized under the free-energy principle, which suggests that several global brain theories might be unified within a free-energy framework.

/pdf/the-free-energy-principle-a-unified-brain-theory-3vz1twg7nv.pdf

The free-energy principle: a unified brain theory?

Threshold-free cluster enhancement: Addressing problems of smoothing, threshold dependence and localisation in cluster inference

One of the core problems of modern statistics is to approximate difficult-to-compute probability densities. This problem is especially important in Bayesian statistics, which frames all inference about unknown quantities as a calculation involving the posterior density. In this article, we review variational inference (VI), a method from machine learning that approximates probability densities through optimization. VI has been used in many applications and tends to be faster than classical methods, such as Markov chain Monte Carlo sampling. The idea behind VI is to first posit a family of densities and then to find a member of that family which is close to the target density. Closeness is measured by Kullback–Leibler divergence. We review the ideas behind mean-field variational inference, discuss the special case of VI applied to exponential family models, present a full example with a Bayesian mixture of Gaussians, and derive a variant that uses stochastic optimization to scale up to massive data...

Variational Inference: A Review for Statisticians

https://www.fil.ion.ucl.ac.uk/~karl/Variational%20free%20energy%20and%20the%20Laplace%20approximation.pdf

Variational free energy and the Laplace approximation

https://www.mrc-cbu.cam.ac.uk/personal/rik.henson/personal/FristonEtAl_NI_08.pdf

Multiple sparse priors for the M/EEG inverse problem

https://www.fil.ion.ucl.ac.uk/~wpenny/publications/vb2_2005.pdf

Bayesian fMRI time series analysis with spatial priors.

https://www.fil.ion.ucl.ac.uk/~karl/DEM%20A%20variational%20treatment%20of%20dynamic%20systems.pdf

DEM: a variational treatment of dynamic systems.

https://stuff.mit.edu/people/ppurdon/BMA_science.pdf

Nelson J. Trujillo-Barreto

Papers

Variational free energy and the Laplace approximation

Multiple sparse priors for the M/EEG inverse problem

Bayesian fMRI time series analysis with spatial priors.

DEM: a variational treatment of dynamic systems.

Bayesian model averaging in EEG/MEG imaging.