New statistical techniques for the analysis of eruption data

This thesis is composed of three independent manuscripts. The common thread among them is the goal to improve and expand on the limited statistical methods available in the literature for the analysis of the temporal distribution of volcanic eruptions, especially when assessing if it is influenced by external factors, such as climate proxies.
The first manuscript (Section 2) aims to present some of our newly developed methodology with an application to the analysis of the eruption record derived from IODP Hole 350-1437B, from the Izu-Bonin arc, in conjunction with the LR04 δ18O global stack as a climate proxy. Based on point processes, we develop models for eruption rate that incorporate information from external factors and propose a novel bootstrap based goodness-of-fit test for parametric point processes. This test is used to evaluate the hypothesis that the δ18O record affects the occurrence of eruptions, and the results suggest that the response to climate change may depend significantly on the magma composition of the events.
The second manuscript (Section 3) provides the mathematical theory behind the goodness-of-fit test mentioned above. Based on recently developed bootstrap techniques and previous works on the asymptotic normality of the maximum likelihood estimator for point processes, the consistency of our test can be proved for the class of inhomogeneous Poisson processes. Nevertheless, it has been empirically verified that this procedures is valid for a much broader range of processes.
The third, and last, manuscript (Section 4) analyzes the thickness and frequency of event beds from different sites to assess possible physical mechanisms modulating their distributions. In particular, the detection of periodicities in the event bed
records were evaluated using methods developed in this project, leveraging the use of simulation to address the significance of the findings.

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