Cuder, María (2025) Exploring Prosperity through Bayesian Networks: A Data-Driven Analysis of the Legatum Prosperity Index. Bachelor's Thesis, Mathematics.
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Abstract
This thesis examines how Gaussian Bayesian Networks (GBNs), a type of probabilistic graphical model that assumes continuous variables have a Gaussian distribution, can model the relationships among the 14 continuous pillars of the 2023 Legatum Prosperity Index. We use the 'bnlearn' R package and apply score-based hill-climbing, a search algorithm for structure learning, using AIC (Akaike Information Criterion) and BIC (Bayesian Information Criterion) scoring methods. For each, we test several restart settings (1, 10, 100, 1000) to assess how stable and sensitive the model structures are. Building on this methodology, we evaluate the models in two ways: structurally, by looking at edge counts, v-structures, Markov blankets, Structural Hamming Distance (SHD), and the Jaccard index; and predictively, using log-likelihood and 5-fold cross-validation. The AIC-G models produce denser networks and slightly better predictions, while the BIC-G models are sparser and more stable. Results from cross-validation show only small differences in performance, suggesting that the main structural findings are reliable, even when model complexity changes.
| 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: | 28 Jul 2025 10:57 |
| Last Modified: | 28 Jul 2025 10:57 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/36559 |
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