An introduction to variational methods for graphical models
Learning in graphical models
Variational Bayes for generalized autoregressive models
IEEE Transactions on Signal Processing
Bayesian methods for fMRI time-series analysis using a nonstationary model for the noise
IEEE Transactions on Information Technology in Biomedicine - Special section on new and emerging technologies in bioinformatics and bioengineering
Hierarchical Bayesian inference for Ill-posed problems via variational method
Journal of Computational Physics
Variational bayes for a mixed stochastic/deterministic fuzzy filter
IEEE Transactions on Fuzzy Systems
A variational Bayesian method to inverse problems with impulsive noise
Journal of Computational Physics
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Variational Bayes (VB) has been proposed as a method to facilitate calculations of the posterior distributions for linear models, by providing a fast method for Bayesian inference by estimating the parameters of a factorized approximation to the posterior distribution. Here a VB method for nonlinear forward models with Gaussian additive noise is presented. In the case of noninformative priors the parameter estimates obtained from this VB approach are identical to those found via nonlinear least squares. However, the advantage of the VB method lies in its Bayesian formulation, which permits prior information to be included in a hierarchical structure and measures of uncertainty for all parameter estimates to be obtained via the posterior distribution. Unlike other Bayesian methods VB is only approximate in comparison with the sampling method of MCMC. However, the VB method is found to be comparable and the assumptions made about the form of the posterior distribution reasonable. Practically, the VB approach is substantially faster than MCMC as fewer calculations are required. Some of the advantages of the fully Bayesian nature of the method are demonstrated through the extension of the noise model and the inclusion of Automatic Relevance Determination (ARD) within the VB algorithm.