Differentiable Bayesian inference of SDE parameters using a pathwise series expansion of Brownian motion

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2 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)10982-10998
Number of pages17
JournalProceedings of Machine Learning Research
Publication statusPublished - 2022
Event25th International Conference on Artificial Intelligence and Statistics, AISTATS 2022 - Virtual, Online, Spain
Duration: 28 Mar 202230 Mar 2022

Bibliographical note

Funding Information:
We like to thank the anonymous reviewers for their helpful comments and suggestions. SG was supported by the Medical Research Council (Unit programme number MC UU 00002/11).

Publisher Copyright:
Copyright © 2022 by the author(s)


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