ArticlePhysica D. Nonlinear phenomena2009
Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models.
Article in Physica D. Nonlinear phenomena, 2009. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 87 papers.
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Who cites it
87 citing papers in PubMed.
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- Network Diffusion Modeling in Computational Neuroscience.Advances in experimental medicine and biology · 2026Article
- BSD: A Bayesian Framework for Parametric Models of Neural Spectra.The European journal of neuroscience · 2025Article
- The human reward system encodes the subjective value of ideas during creative thinking.Communications biology · 2025Article
- Do Human Reinforcement Learning Models Account for Key Experimental Choice Patterns in the Iowa Gambling Task?Computational brain & behavior · 2025Article
- Transformer-aided dynamic causal model for scalable estimation of effective connectivity.Imaging neuroscience (Cambridge, Mass.) · 2024Article
- Stochastic attractor models of visual working memory.PloS one · 2024Article
- Linking fast and slow: The case for generative models.Network neuroscience (Cambridge, Mass.) · 2024Review
- Dynamic Effective Connectivity using Physiologically informed Dynamic Causal Model with Recurrent Units: A functional Magnetic Resonance Imaging simulation study.Frontiers in human neuroscience · 2023Article
- A Glucose-Only Model to Extract Physiological Information from Postprandial Glucose Profiles in Subjects with Normal Glucose Tolerance.Journal of diabetes science and technology · 2022Article
- A neuro-computational account of procrastination behavior.Nature communications · 2022Article
- Is Resting State Functional MRI Effective Connectivity in Movement Disorders Helpful? A Focused Review Across Lifespan and Disease.Frontiers in neurology · 2022Review
- Gradient Regularization as Approximate Variational Inference.Entropy (Basel, Switzerland) · 2021Article
- Inference of brain networks with approximate Bayesian computation - assessing face validity with an example application in Parkinsonism.NeuroImage · 2021Article
- Regression dynamic causal modeling for resting-state fMRI.Human brain mapping · 2021Article
- Computational and Neurobiological Substrates of Cost-Benefit Integration in Altruistic Helping Decision.The Journal of neuroscience : the official journal of the Society for Neuroscience · 2021Article
- Parallel cortical-brainstem pathways to attentional analgesia.NeuroImage · 2021Article
- Neuronal Sequence Models for Bayesian Online Inference.Frontiers in artificial intelligence · 2021Review
27 more citing papers are in PubMed but not listed here.
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Authors and funding
3 authors.
Funding
Abstract
In this paper, we describe a general variational Bayesian approach for approximate inference on nonlinear stochastic dynamic models. This scheme extends established approximate inference on hidden-states to cover: (i) nonlinear evolution and observation functions, (ii) unknown parameters and (precision) hyperparameters and (iii) model comparison and prediction under uncertainty. Model identification or inversion entails the estimation of the marginal likelihood or evidence of a model. This difficult integration problem can be finessed by optimising a free-energy bound on the evidence using results from variational calculus. This yields a deterministic update scheme that optimises an approximation to the posterior density on the unknown model variables. We derive such a variational Bayesian scheme in the context of nonlinear stochastic dynamic hierarchical models, for both model identification and time-series prediction. The computational complexity of the scheme is comparable to that of an extended Kalman filter, which is critical when inverting high dimensional models or long time-series. Using Monte-Carlo simulations, we assess the estimation efficiency of this variational Bayesian approach using three stochastic variants of chaotic dynamic systems. We also demonstrate the model comparison capabilities of the method, its self-consistency and its predictive power.
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Registered trials
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.