Forecasting Future Eruptions Using Hierarchical Trend Renewal Processes

Joel Carman, Ting Wang, Mark Bebbington, Shane Cronin, Marco Brenna and Ingrid Ukstins

The American Statistician, 2026, vol. 80, issue 2, 265-276

Abstract: Forecasting volcanic eruptions can be challenging due to the typically sparse and incomplete data available in geological and/or historical eruption records. This leads to analysis of volcanoes with comparable physical properties and statistical behavior (eruption recurrence) to a target volcano. Analogue patterns are thus used to estimate model parameters and forecast future eruptions. This approach, however, often fails to consider the specific problem of “missing data”, which is common due to the uncertain and possibly unknowable processes in geologic records over thousands to tens of thousands of years. To approach this problem, we propose a set of hierarchical trend renewal processes to model analogue volcanoes to account for missing data. From these we create a Bayesian model averaging scheme for forecasting. This incorporates model uncertainty by combining the posterior distribution of the forecast times from each of the considered models. We apply this method to forecasting eruptions from Mt Taranaki in New Zealand, which last erupted in ∼1780 AD and has its entire eruption record only preserved in geological deposits.

Date: 2026
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DOI: 10.1080/00031305.2025.2540590

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