Stochastic Variational Bayesian Inference for a Nonlinear Forward Model
This work provides a more flexible inference method for researchers in fields like medical imaging, though it is incremental as it builds on existing variational Bayes approaches.
The authors tackled the problem of Bayesian inference for nonlinear models by developing a stochastic variational Bayes method that avoids approximations required by previous analytical formulations, achieving comparable parameter recovery and competitive computational speed on both synthetic and real MRI perfusion data.
Variational Bayes (VB) has been used to facilitate the calculation of the posterior distribution in the context of Bayesian inference of the parameters of nonlinear models from data. Previously an analytical formulation of VB has been derived for nonlinear model inference on data with additive gaussian noise as an alternative to nonlinear least squares. Here a stochastic solution is derived that avoids some of the approximations required of the analytical formulation, offering a solution that can be more flexibly deployed for nonlinear model inference problems. The stochastic VB solution was used for inference on a biexponential toy case and the algorithmic parameter space explored, before being deployed on real data from a magnetic resonance imaging study of perfusion. The new method was found to achieve comparable parameter recovery to the analytic solution and be competitive in terms of computational speed despite being reliant on sampling.