Computational aspects of hierarchical mixture models for geological data

• Main Author: Laidlaw, Michaela
• Other Authors: Bekker, Andriette, 1958-
• Published: University of Pretoria 2021
• Subjects: UCTD
• Online Access: http://hdl.handle.net/2263/78378

Buidling off a foundation of knowledge from studies into modelling wind speed, models are fitted to multimodal datasets of geological nature. Mixtures of distributions are derived with parameter updates done via implementation of the EM algorithm. Among these mixtures is the Birnbaum-Saunders which is used as a component of hierarchical mixture of multiple distributions for the first time. The derivations of parameter updates in the EM algorithm setting is done and application to five real world datasets, one of which is large, implemented whilst keeping computation in mind. Additionally a simulation study is done for the mixtures of distributions with results indicating larger samples result in better fit whilst not compromising runtimes. Simulation studies for hierarcical mixtures to be considered in future work as obtaining convergence is challenging. === Dissertation (MSc (Mathematical Statistics))--University of Pretoria, 2021. === SRUG190308422768 grant No. 120839 and NRF GRANT : VULNERABLE DISCIPLINE: ACADEMIC STATISTICS (STATS). === Statistics === MSc (Mathematical Statistics) === Restricted