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Flexible Bayesian Inference for Diffusion Processesusing Splines

Lookup NU author(s): Professor Murray Pollock

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Abstract

© 2023, Crown. We introduce a flexible method to simultaneously infer both the drift and volatility functions of a discretely observed scalar diffusion. We introduce spline bases to represent these functions and develop a Markov chain Monte Carlo algorithm to infer, a posteriori, the coefficients of these functions in the spline basis. A key innovation is that we use spline bases to model transformed versions of the drift and volatility functions rather than the functions themselves. The output of the algorithm is a posterior sample of plausible drift and volatility functions that are not constrained to any particular parametric family. The flexibility of this approach provides practitioners a powerful investigative tool, allowing them to posit a variety of parametric models to better capture the underlying dynamics of their processes of interest. We illustrate the versatility of our method by applying it to challenging datasets from finance, paleoclimatology, and astrophysics. In view of the parametric diffusion models widely employed in the literature for those examples, some of our results are surprising since they call into question some aspects of these models.

Publication metadata

Author(s): Jenkins PA, Pollock M, Roberts GO

Publication type: Article

Publication status: Published

Journal: Methodology and Computing in Applied Probability

Year: 2023

Volume: 25

Issue: 4

Online publication date: 27/10/2023

Acceptance date: 29/08/2023

ISSN (print): 1387-5841

ISSN (electronic): 1573-7713

Publisher: Springer Nature

URL: https://doi.org/10.1007/s11009-023-10056-9

DOI: 10.1007/s11009-023-10056-9

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