Accelerating inference for diffusions observed with measurement error and large sample sizes using approximate Bayesian computation

Abstract

In recent years, dynamical modelling has been provided with a range of breakthrough methods to perform exact Bayesian inference. However, it is often computationally unfeasible to apply exact statistical methodologies in the context of large data sets and complex models. This paper considers a nonlinear stochastic differential equation model observed with correlated measurement errors and an application to protein folding modelling. An approximate Bayesian computation (ABC)-MCMC algorithm is suggested to allow inference for model parameters within reasonable time constraints. The ABC algorithm uses simulations of ‘subsamples’ from the assumed data-generating model as well as a so-called ‘early-rejection’ strategy to speed up computations in the ABC-MCMC sampler. Using a considerate amount of subsamples does not seem to degrade the quality of the inferential results for the considered applications. A simulation study is conducted to compare our strategy with exact Bayesian inference, the latter resulting two orders of magnitude slower than ABC-MCMC for the considered set-up. Finally, the ABC algorithm is applied to a large size protein data. The suggested methodology is fairly general and not limited to the exemplified model and data.

Keywords:

• likelihood-free inference
• MCMC
• protein folding
• stochastic differential equation

AMS Subject Classification:

• 62M09
• 62F15
• 60J60
• 92C40

Acknowledgments

We are grateful to Sandro Bottaro and Jesper Ferkinghoff-Borg, Elektro DTU, for supplying the data for the case study. We thank an anonymous reviewer for providing useful suggestions that improved the present work.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. http://xianblog.wordpress.com/2013/10/17/accelerated-abc/.

Additional information

Funding

Umberto Picchini and Julie Forman research is partly funded by a grant from the Swedish Research Council (VR grant 2013-5167).