https://www.um.edu.mt/library/oar/handle/123456789/113273 2026-04-28T07:40:56Z 2026-04-28T07:40:56Z https://www.um.edu.mt/library/oar/handle/123456789/126895 2024-09-24T10:38:01Z 2023-01-01T00:00:00Z

Title: Bayesian parameter estimation of the hurst index of fractional brownian motion Abstract: One of the many generalizations of Brownian Motion, Fractional Brownian Motion is very popular due to being able to account for a wide range of phenomena in various different fields ranging from finance when modelling stock data to hydrology in water turbidity analysis. Brownian Motion is unsuitable for modelling these due to the assumption of independence of increments, an assumption relaxed by Fractional Brownian Motion given it allows dependence of increments. This dependence is effected through the Hurst Index H, the parameter associated with the process. For values of H between 0 and 0.5, both excluded, negative autocorrelation between the increments is enforced while a positive one is obtained for values between 0.5 and 1, both excluded. As H approaches 0.5, the paths of the process will resemble those given by Brownian Motion and if equality holds, the process reduces to a Brownian Motion Process. In this thesis, the theory behind Fractional Brownian Motion as well as the Bayesian framework in the context of estimating H shall be discussed. Given the subjectivity involved in determining a prior, sensitivity analysis shall be performed as to analyze the effect of different priors on the posterior. Following this, the Hurst Index of real data shall be estimated. The data considered shall be genetic data relating to Covid-19 and cardiology data relating to heart rate variation. Description: B.Sc. (Hons)(Melit.)

2023-01-01T00:00:00Z https://www.um.edu.mt/library/oar/handle/123456789/126820 2024-09-23T05:50:11Z 2023-01-01T00:00:00Z

Title: Estimation of the hubble constant using Gaussian process regression and viable alternatives Abstract: Several papers within the astrophysical literature are dedicated to obtaining accurate and reliable estimates for the Hubble constant H0, using diverse data sources such as CC, SNIa, and BAO, and different methodologies. This results in estimates which do not agree with each other - the so-called ‘H0 tension’. In this work, methods already established in literature for estimating H0, such as Gaussian process regression (GPR) and Markov chain Monte Carlo (MCMC) methods based on the concordance Lambda Cold Dark Matter (ΛCDM) model, together with some novel approaches in the field, are assessed. The first novel approach makes use of non-parametric MCMC inference on the hyperparameters of a Gaussian process kernel, independently of any cosmological model such as ΛCDM. The second approach is Student’s t-process regression (TPR), which is similar to GPR but makes use of the multivariate Student’s t-distribution instead of the multivariate Gaussian distribution. TPR does not automatically assume Gaussianity of underlying observations and has the additional advantage of being a more generalised and flexible form of GPR. We also consider variants of GPR and TPR which account for heteroscedasticity within the data. A comparison of the novel and tried-and-tested approaches is made. In particular, the model-independent approaches investigated largely agree with predictions based on the ΛCDM concordance model. Moreover, GPR is highly dependent on the prior specification, while TPR and the heteroscedastic variants of both GPR and TPR are more robust to this. TPR and both heteroscedastic models provide evidence for a Hubble constant value that is on the lower side, and is therefore closer to the Planck value of 67.4 km s-1 Mpc-1 than the Riess value of 74.22 km s-1 Mpc-1. Therefore, the novel approaches discussed in this dissertation may shed further light on the H0 tension. A main challenge posed by these approaches is the use of small datasets for the model-independent approaches; further research can thus apply such approaches to larger datasets. Across all estimates obtained for H0 in this work, the median value is Hˆ med 0 = 68.85 ± 1.67 km s-1 Mpc-1. Description: M.Sc.(Melit.)

2023-01-01T00:00:00Z https://www.um.edu.mt/library/oar/handle/123456789/126819 2024-09-23T05:49:10Z 2023-01-01T00:00:00Z

Title: Univariate and multivariate extreme value analysis of Düsseldorf hydrological data Abstract: The rise in catastrophic climate events during the late 20th century prompted an increase in the application of statistical methods based on extreme value theory (EVT) in the fields of hydrology, climate, and meteorology. Several statistical models have been developed over the years. This dissertation presents an in-depth review of the fundamental univariate and multivariate techniques that rely on asymptotic EVT results. This dissertation focuses on univariate methods, including the Block Maxima (BM) method, the K largest Order Statistics (KLOS) method, and the Peak over Threshold (POT) method. Also, the Component-wise Block Maxima (CWBM) method and the General Copula-based (GCB) method are covered as multivariate methods. These methods are applied to the monthly mean of river discharge observations and the collective impact of snow melt and precipitation excess observations that were collected from Düsseldorf stations. Through these models, the return period and return level metrics are used to assess whether flood risk mitigation measures are sufficient for Düsseldorf and if the univariate analysis is still important to be taken into consideration when implementing flood protection measures in light of the inter-relationship between extreme events. Description: M.Sc.(Melit.)

2023-01-01T00:00:00Z https://www.um.edu.mt/library/oar/handle/123456789/126581 2024-09-12T11:01:27Z 2023-01-01T00:00:00Z

Title: Rooting out deception : the application of tree-based learners for motor insurance fraud detection Abstract: This dissertation investigates motor insurance fraud detection in the Spanish market by implementing and comparing tree-based methods, renowned for their performance and interpretability. The study begins with basic Decision Trees and progresses to tree-based ensemble methods, including Random Forests, Gradient Boosting machines, and Newton-based boosting techniques such as LightGBM, XGBoost, and CatBoost. A significant challenge in motor insurance fraud detection is addressing the class imbalance. To address this issue, the dissertation evaluates cost-sensitive learning approaches and resampling techniques to optimize model performance. The analysis concludes that a cost-sensitive LightGBM model is the most effective method for this scenario, achieving a balanced accuracy of 81% and successfully identifying 83% of fraudulent cases. The findings of this study provide valuable insights into the effectiveness of tree-based methods in detecting motor insurance fraud and highlight the potential of LightGBM in efficiently identifying fraudulent cases. By presenting a rigorous comparison of different techniques and addressing the class imbalance issue, this research contributes to the ongoing development of interpretable solutions for combating insurance fraud. Description: B.Sc.(Melit.)

2023-01-01T00:00:00Z