Hoh, Tjun Yee;
(2019)
Bayesian inference and model selection for multi-dimensional diffusion process models with non-parametric drift and constant diffusivity.
Doctoral thesis (Ph.D), UCL (University College London).
Preview |
Text
tyh_finalthesis_250619.pdf Download (11MB) | Preview |
Abstract
For a multi-dimensional, partially observed diffusion process model with unknown drift and variable-independent diffusivity, we construct a composite methodology to perform Bayesian inference for the coefficients. Recent development of non-parametric Bayesian estimation of the drift has been restricted to dimension one, since the local time process is unavailable in the multi-dimensional case. We involve the empirical measure instead and show that the drift likelihood has a quadratic form, which allows a conjugate Gaussian measure prior whose precision operator is chosen to be a high order differential operator. We detail a computationally efficient pseudo-spectral method for solving the posterior mean, and describe how inference for the drift can be constrained to allow only conservative drifts. We also adapt a Langevin MCMC approach to sampling from diffusion bridges as a data augmentation scheme. To sample from the diffusivity, we specify an Inverse Wishart prior and implement a random walk Metropolis-Hastings algorithm. Evaluation of model fit for diffusion processes historically involved frequentist goodness-of-fit testing for fully parametric null models. We extend an existing transition density-based omnibus test to the null model case with non-parametric drift. We study the finite-sample behaviour of the test statistic and show that existing asymptotic results are inappropriate for settings involving real data. We implement the Bayesian discrepancy p-value to complement our inference methodology. With the goal of model improvement in mind, we describe how outlier removal and systematic sub-sampling of the data can be beneficial.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | Bayesian inference and model selection for multi-dimensional diffusion process models with non-parametric drift and constant diffusivity |
| Event: | UCL (University College London) |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Additional information: | Copyright © The Author 2019. Original content in this thesis is licensed under the terms of the Creative Commons Attribution 4.0 International (CC BY 4.0) Licence (https://creativecommons.org/licenses/by/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. Access may initially be restricted at the author’s request. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10076641 |
Archive Staff Only
 |
View Item |
