Inference for Hawkes processes with challenging data

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The Hawkes processes are statistical models for the analysis of high-impact event sequences, such as bushfires, earthquakes, infectious diseases, and cyber attacks. When the times and/or marks are missing for some events or when the data is otherwise incomplete, it is challenging to fit these models and perform diagnostic checks on the fitted models. This project aims to develop novel statistical methods to fit these models in the presence of incomplete data and to check the goodness-of-fit of the fitted models. The expected outcomes include publications documenting these methods and software packages implementing them. The primary benefits include the advancement of statistical methodology and the training of junior research personnel.