Differentiable Bayesian Inference of SDE Parameters Using a Pathwise Series Expansion of Brownian Motion
Abstract
By invoking a pathwise series expansion of Brownian motion, we propose to approximate a stochastic differential equation (SDE) with an ordinary differential equation (ODE). This allows us to reformulate Bayesian inference for a SDE as the parameter estimation task for an ODE. Unlike a nonlinear SDE, the likelihood for an ODE model is tractable and its gradient can be obtained using adjoint sensitivity analysis. This reformulation allows us to use an efficient sampler, such as NUTS, that rely on the gradient of the log posterior. Applying the reparameterisation trick, variational inference can also be used for the same estimation task. We illustrate the proposed method on a variety of SDE models. We obtain similar parameter estimates when compared to data augmentation techniques.
Cite
Text
Ghosh et al. "Differentiable Bayesian Inference of SDE Parameters Using a Pathwise Series Expansion of Brownian Motion." Artificial Intelligence and Statistics, 2022.Markdown
[Ghosh et al. "Differentiable Bayesian Inference of SDE Parameters Using a Pathwise Series Expansion of Brownian Motion." Artificial Intelligence and Statistics, 2022.](https://mlanthology.org/aistats/2022/ghosh2022aistats-differentiable/)BibTeX
@inproceedings{ghosh2022aistats-differentiable,
title = {{Differentiable Bayesian Inference of SDE Parameters Using a Pathwise Series Expansion of Brownian Motion}},
author = {Ghosh, Sanmitra and Birrell, Paul J. and De Angelis, Daniela},
booktitle = {Artificial Intelligence and Statistics},
year = {2022},
pages = {10982-10998},
volume = {151},
url = {https://mlanthology.org/aistats/2022/ghosh2022aistats-differentiable/}
}