Bayesian Modelling of Marked Point Processes with Incomplete Records: Volcanic Eruptions

Wang, Ting; Schofield, Matthew; Kiyosugi, Koji

doi:10.1111/rssc.12380

Cited by 9 publications

(10 citation statements)

References 51 publications

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“…This assumption could potentially underestimate the hazard if some VEI ≥ 3 eruptions were missing from the records. While this important issue has been studied (e.g., Mead & Magill, 2014; Wang & Bebbington, 2012, 2013; Wang et al., 2020), the solutions all require either a long homogeneous record, or a very large set of volcanoes. Previous studies on missing data make simple assumptions, such as the global large volcanic eruptions following a Poisson process, or the probabilities of an eruption missing from a record dependent only on time (or region, time and VEI).…”

Section: Discussionmentioning

confidence: 99%

Forecasting Eruptions at Poorly Known Volcanoes Using Analogs and Multivariate Renewal Processes

Wang

Cronin

Carman

2022

Geophysical Research Letters

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Eruptions from re-awakening volcanoes can threaten life and infrastructure, and disrupt the economy, particularly after long periods of dormancy (e.g., Soufrière Hills, Montserrat, Weidner et al., 2001; Pinatubo, Philippines, Newhall, & Punongbayan, 1996). In the vast majority of cases, there is limited amount of data available for either geological or historical evidence of past volcanism (Loughlin et al., 2015). This makes robust estimation of eruptive hazard from individual volcanoes very challenging and limits the performance of probabilistic forecasting models of any type (e.g.

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Section: Discussionmentioning

confidence: 99%

Forecasting Eruptions at Poorly Known Volcanoes Using Analogs and Multivariate Renewal Processes

Wang

Cronin

Carman

2022

Geophysical Research Letters

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“…Whilst we did not see the same uncertainty with the Distributed Cones and Fields class within the A2 classification system, there are far fewer volcanoes within the A2 system (n = 341 vs. n = 19) and so this may explain why there is less variability. It should also be noted that reduced diversity of volcanoes at a regional level compared to the global level may mean that mixing across relatively few volcanoes is not sufficient to support a Poisson approximation (Bebbington and Lai 1996;Bebbington 2007;Rougier et al, 2018a;Wang et al, 2020). This may suggest that the transferability of characteristics between volcano analogue classifications that have few numbers of individual volcanoes may require a more considered approach than the relatively simple schemas used in this work.…”

Section: Uncertainty In Frequency-magnitude Estimates For Southeast A...mentioning

confidence: 96%

“…For example, many volcanoes around the world have poorly characterised and incomplete eruption histories (Loughlin et al, 2015). Work at relatively well-studied volcanoes demonstrates that it can take a long, sustained, and resource intensive research effort to build high quality eruption catalogues at the individual volcano scale (Turner et al, 2008;Damaschke et al, 2017;Crummy et al, 2019); however, the level of completeness that can be achieved will vary around the world as a function of climatic conditions, eruption style, and duration of written records (Brown et al, 2014;Rougier et al, 2016;Rougier et al, 2018b;Wang et al, 2020). This raises the question: how can eruption probabilities be derived for volcanoes with little or no eruption records?…”

Section: Introductionmentioning

confidence: 99%

Large Uncertainties Are Pervasive in Long-Term Frequency-Magnitude Relationships for Volcanoes in Southeast Asia

2022

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Frequency-magnitude relationships are a fundamental aspect of volcanic hazard and risk analysis. Typically, frequencies of previously recorded eruptions are used to identify such relationships. This works well for volcanoes that are well-studied, but it can take a long, sustained, and resource intensive research effort to compile complete eruption records. Further, the level of completeness that can be achieved will vary around the world as a function of climatic conditions, eruption style, and duration of written records. Given the importance of understanding hazard and risk for disaster risk reduction, how can frequency-magnitude relationships be determined for volcanoes with little or no eruption records? Analogue models have been used to supplement the eruption records of volcanoes with limited or no recorded eruptions. However, there has been little effort undertaken to compare the agreeability of different approaches to estimating frequency-magnitude relationships using these analogue models. This has implications for volcanic hazard and risk assessment, if different approaches are considered credible, yet yield vastly different estimates. In this work we compare frequency-magnitude relationships for volcanoes in Southeast Asia, a region where eruption records are known to be very incomplete. We do this by first reviewing published frequency-magnitude relationships to evaluate the agreeability between different approaches, and then develop a top-down multi-model Bayesian updating approach to deriving frequency-magnitude relationships for a wide variety of volcanoes in Southeast Asia (n = 176). Our review of published estimates found that there is considerable variability between published eruption probabilities for volcanoes in Southeast Asia. We also found that using different analogue models in the Bayesian analysis can lead to considerably different frequency-magnitude relationships (over an order of magnitude in some cases), highlighting the importance of using multiple models to ensure robust probability estimations are obtained. Sensitivity analysis demonstrated that the choice of model averaging or model combination method can influence the resulting frequency-magnitude estimations, whilst the choice to incorporate or remove uncertain eruption records had modest or no effect. Our findings provide important considerations for estimating frequency-magnitude relationships in volcanic hazard and risk assessments, and a method to combine multiple frequency-magnitude models whilst accounting for uncertainty in our estimations.

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“…The major difficulty in analytically deriving the posterior distribution comes from the difficulty in calculating the value of P (θ) even though it is a constant. Green et al, 2016;Anderson et al, 2019;Covey et al, 2019;Lev et al, 2019;Jenkins et al, 2019;Wang et al, 2020;Liang and Dunham, 2020). Green et al (2016) used one MCMC method to estimate volumes of tephra fall deposits based on sparse and incomplete observations, and their work used a semi-empirical model to characterize tephra thickness distribution.…”

Section: Bayes' Rulementioning

confidence: 99%

Tephra Deposit Inversion by Coupling TEPHRA2 With the Metropolis-Hastings Algorithm and Its Implications

Yang¹,

Pitman²,

Bursik³

et al. 2020

Preprint

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Abstract In this work we couple the Metropolis-Hastings algorithm with the volcanic ash transport model TEPHRA2, and present the coupled algorithm as a new method to estimate the Eruption Source Parameters of volcanic eruptions based on mass per unit area or thickness measurements of tephra fall deposits. Basic elements in the algorithm and how to implement it are introduced. Experiments are done with synthetic datasets. These experiments are designed to demonstrate that the algorithm works, and to show how inputs affect its performance. Results are presented as sample posterior distribution estimates for variables of interest. Advantages of the algorithm are that it has the ability to i) incorporate prior knowledge; ii) quantify the uncertainty; and iii) capture correlations between variables of interest in the estimated Eruption Source Parameters. A limitation is that some of the inputs need to be specifed subjectively. How and why such inputs affect the performance of the algorithm and how to specify them properly are explained and listed. Correlation between variables of interest are well-explained by the physics of tephra transport. We point out that in tephra deposit inversion, caution is needed in attempting to estimate Eruption Source Parameters, and wind direction and speed at each elevation level, as this increases the number of variables to be estimated. The algorithm is applied to a mass per unit area dataset of the tephra deposit from the 2011 Kirishima-Shinmoedake eruption. Simulation results from TEPHRA2 using posterior means from the algorithm are consistent with field observations, suggesting that this approach reliably reconstructs Eruption Source Parameters and wind conditions from the deposit.

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Bayesian Modelling of Marked Point Processes with Incomplete Records: Volcanic Eruptions

Cited by 9 publications

References 51 publications

Forecasting Eruptions at Poorly Known Volcanoes Using Analogs and Multivariate Renewal Processes

Forecasting Eruptions at Poorly Known Volcanoes Using Analogs and Multivariate Renewal Processes

Large Uncertainties Are Pervasive in Long-Term Frequency-Magnitude Relationships for Volcanoes in Southeast Asia

Tephra Deposit Inversion by Coupling TEPHRA2 With the Metropolis-Hastings Algorithm and Its Implications

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