ArticleNeuroImage2023
A primer on Variational Laplace (VL).
Article in NeuroImage, 2023. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 30 papers.
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Who cites it
30 citing papers in PubMed.
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- Disruption of temporo-parietal network in Alzheimer's disease and its association with memory impairment.Alzheimer's research & therapy · 2026Observational
- Limitations of Variational Laplace-Based Dynamic Causal Modelling for Multistable Cortical Circuits.Neuroinformatics · 2026Article
- Understanding mechanisms of voluntary engagement of mental effort using active inference.Cognitive, affective & behavioral neuroscience · 2026Article
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- Structurally informed resting-state effective connectivity recapitulates cortical hierarchy.bioRxiv : the preprint server for biology · 2025Article
- The Criticality of Consciousness: Excitatory-Inhibitory Balance and Dual Memory Systems in Active Inference.Entropy (Basel, Switzerland) · 2025Article
- SPM-30 years and beyond.Cerebral cortex (New York, N.Y. : 1991) · 2025Review
- Spectral imprint of structural embedding in effective connectivity.bioRxiv : the preprint server for biology · 2025Article
- Priors and proprioceptive predictions.Current opinion in behavioral sciences · 2025Article
- Dynamic causal modelling in probabilistic programming languages.Journal of the Royal Society, Interface · 2025Article
- BSD: A Bayesian Framework for Parametric Models of Neural Spectra.The European journal of neuroscience · 2025Article
- Structurally informed models of directed brain connectivity.Nature reviews. Neuroscience · 2025Review
- Increasing spectral DCM flexibility and speed by leveraging Julia's ModelingToolkit and automated differentiation.Imaging neuroscience (Cambridge, Mass.) · 2025Article
- Interhemispheric integration in the neural face perception network: Does stimulus location matter?Imaging neuroscience (Cambridge, Mass.) · 2025Article
- Estimating the value of face coverings during the COVID-19 epidemic: a dynamic causal modelling study.BMJ public health · 2025Article
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3 authors.
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Abstract
This article details a scheme for approximate Bayesian inference, which has underpinned thousands of neuroimaging studies since its introduction 15 years ago. Variational Laplace (VL) provides a generic approach to fitting linear or non-linear models, which may be static or dynamic, returning a posterior probability density over the model parameters and an approximation of log model evidence, which enables Bayesian model comparison. VL applies variational Bayesian inference in conjunction with quadratic or Laplace approximations of the evidence lower bound (free energy). Importantly, update equations do not need to be derived for each model under consideration, providing a general method for fitting a broad class of models. This primer is intended for experimenters and modellers who may wish to fit models to data using variational Bayesian methods, without assuming previous experience of variational Bayes or machine learning. Accompanying code demonstrates how to fit different kinds of model using the reference implementation of the VL scheme in the open-source Statistical Parametric Mapping (SPM) software package. In addition, we provide a standalone software function that does not require SPM, in order to ease translation to other fields, together with detailed pseudocode. Finally, the supplementary materials provide worked derivations of the key equations.
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Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.