Parameter Estimation on the Partially Observed Bidimensional Ornstein-Uhlenbeck Process

Parameter Estimation on the Partially Observed Bidimensional Ornstein-Uhlenbeck Process

Qin, Ziqiu (TU Delft Electrical Engineering, Mathematics and Computer Science)

van der Meulen, F.H. (mentor)
Heemink, A.W. (graduation committee)
Kekkonen, H.N. (graduation committee)

Delft University of Technology

Applied Mathematics | Financial Engineering

2022-11-03

In anti-cancer therapy, ntiangiogenic treatments are applied and take effect on the vascularization of tissue. To evaluate the efficacy of treatments, we adopt two methods to solve the physiological pharmacokinetic model’s parameter estimation problem, providing discrete, partial, and noisy observations of stochastic differential equations. One is to compute the exact likelihood using the Kalman filter recursion and implement numerical maximization. The other is a novel Markov Chain Monte Carlo algorithm to estimate parameters using guided proposals in a Bayesian setup, namely Backward Filtering with Forward Guiding algorithm. The identifiability of the model and parameters are established before parametric inference. We extend the BFFG algorithm to include an automatic optimal kernel finding scheme for the Metropolis-Hastings-within-Gibbs sampler. In comparison, a Conjugate Gradient algorithm is applied when employing the maximum likelihood method. Besides performing parameter estimation via different methods separately, joint estimation is performed using the Bayesian approach. After that, time delay and Arterial Input Function in the statistical model are estimated via change point detection and piecewise inference. We illustrate the goodness-of-fit of estimates and advantages of the bayesian approach towards the maximum likelihood method.

Identifiability Analysis
Bayesian Inference
Change Point Estimation

http://resolver.tudelft.nl/uuid:0077e663-32dd-4583-aae3-69bf6eac7017

2024-11-03

Student theses

master thesis

© 2022 Ziqiu Qin