Supervisors: Dr Adam Sykulski (ICL)and Dr James Martin
Project Description:
Jakub’s interest is in spatio-temporal statistics. During his PhD, he explores various topics in this area.
His first project focused on spatial point patterns, a type of data common in fields such as ecology. Jakub’s work concerned test for isotropy, an assumption that underlying processes behave the same in all directions. Such assumption is commonly made in modelling of spatial point patterns. He developed a general nonparametric testing framework. In an extensive simulation study, he used it to compare tests which make assumptions regarding underlying models with those that circumvent such assumptions. He particularly focused on cases when underlying models are difficult to identify and therefore may be easily misspecified in practice.
In his current project, Jakub collaborates with the British Geological Survey on models for groundwater levels which improve understanding of processes driving such hazards as groundwater droughts. Jakub is developing an alternative estimation method to replace traditional maximum likelihood. The new estimation method will handle incomplete time series, typical for groundwater level measurements, and will be more robust to model misspecification than maximum likelihood. Additionally, the new method will be less computationally complex, and thus more appropriate for large datasets.
