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Title: Bayesian inference and model selection for multi-dimensional diffusion process models with non-parametric drift and constant diffusivity
Author: Hoh, Tjun Yee
ISNI:       0000 0004 7965 1745
Awarding Body: UCL (University College London)
Current Institution: University College London (University of London)
Date of Award: 2019
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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.
Supervisor: Pokern, Y. ; Beskos, A. ; Chandler, R. Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available