Variational free energy and the Laplace approximation

K Friston, J Mattout, N Trujillo-Barreto, J Ashburner…�- Neuroimage, 2007 - Elsevier
Variational Bayes, under the Laplace approximation, assumes a fixed Gaussian form for the
… summarise the basic theory of variational Bayes and apply it in the context of the Laplace

[BOOK][B] Variational bayes

W Penny, S Kiebel, K Friston - 2006 - books.google.com
… The theoretical section is completed by relating VB to Laplace approximationsBayesian
model comparison. Numerical examples are then given showing how VB differs from Laplace

[HTML][HTML] A primer on Variational Laplace (VL)

P Zeidman, K Friston, T Parr�- NeuroImage, 2023 - Elsevier
variational Bayesian inference in conjunction with quadratic or Laplace approximations of
the … of quadratic approximations and Laplace's method, which we will first reprise. A quadratic …

The variational Laplace approach to approximate Bayesian inference

J Daunizeau�- arXiv preprint arXiv:1703.02089, 2017 - arxiv.org
… that complete the portfolio of existing analyses of variational Bayesian approaches, … Laplace
approximation to go from the first to the second line, and the expression for the variational

[PDF][PDF] The FMRIB variational Bayes tutorial: Variational Bayesian inference for a non-linear forward model

M Chappell, A Groves, M Woolrich - 2016 - ora.ox.ac.uk
Friston et al. (2007) have also applied their variational Laplace method to non-linear models
by way of a Taylor expansion, this time assuming that the model is weakly non-linear and …

Variational filtering

KJ Friston�- NeuroImage, 2008 - Elsevier
Variational Bayes also provides a lower-… inference on the states of a linear convolution
model. The only difference is that here, we have used a Laplace approximation to the variational

[PDF][PDF] The fmrib variational bayes tutorial

MA Chappell, A Groves, MW Woolrich�- Rapport technique, FMRIB�…, 2008 - academia.edu
Friston et al. (2007) have also applied their variational Laplace method to non-linear models
by way of a Taylor expansion, this time assuming that the model is weakly non-linear and …

[HTML][HTML] Post hoc Bayesian model selection

K Friston, W Penny�- Neuroimage, 2011 - Elsevier
… parameters of any model (DCM) under the Laplace approximation. In other words, it assumes
that … The variational Bayesian EM algorithm for incomplete Data: with application to scoring …

Bayesian decoding of brain images

K Friston, C Chu, J Mour�o-Miranda, O Hulme, G Rees…�- Neuroimage, 2008 - Elsevier
… is itself a special case of variational Bayes. In fact, these … variational approximation to the
approximating posterior under the Laplace approximation and the mean field approximation

Predictive Coding with Approximate Laplace Monte Carlo

U Zahid, Q Guo, K Friston, Z Fountas - openreview.net
… By adopting the perspective of PC as a variational Bayes algorithm under the Laplace
approximation, we identify the source of these deficits to lie in the exclusion of an associated …