Wieringa, Jelmer (2025) Bayesian Quadrature: Theory and Comparative Simulation Study. Bachelor's Thesis, Mathematics.
|
Text
Bachelors-Thesis-MathematicsBayesian-QuadratureJelmer-Wieringa.pdf Download (18MB) | Preview |
Abstract
Bayesian quadrature (BQ) treats numerical integration as a statistical inference problem by modelling the integrand as a Gaussian process. Applying the integration operator to the Gaussian process and conditioning on observed function values yields a posterior distribution for the value of the integral, rather than merely a point estimate. This thesis presents a formulation of BQ based on the closure of Gaussian processes under bounded linear operators. A systematic comparison is conducted between Monte Carlo (MC) integration, fixed-grid BQ, and uncertainty-sampling BQ under three scenarios: estimating the kernel and hyperparameters once, re-estimating hyperparameters only, and re-estimating both at each iteration. The methods are evaluated on a one-dimensional integral, the marginal likelihood of a Gaussian Bayesian linear regression model, and a synthetic trimodal marginal likelihood with a Gaussian mixture model as likelihood. The BQ methods outperform MC integration only in the well-behaved one-dimensional setting. In more complex applications, kernel misspecification, integrand structure, and instability in hyperparameter estimation reduce the effectiveness of BQ, whereas MC integration remains robust. These results highlight that BQ is a powerful but assumption-sensitive method, whose performance critically depends on the suitability of the chosen prior structure encoded through the kernel.
| Item Type: | Thesis (Bachelor's Thesis) |
|---|---|
| Supervisor name: | Grzegorczyk, M.A. and Krijnen, W.P. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 13 Mar 2026 09:33 |
| Last Modified: | 13 Mar 2026 09:33 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/37255 |
Actions (login required)
 |
View Item |