Rare Event Probability Estimation for Groundwater Inverse Problems With a Two‐Stage Sequential Monte Carlo Approach

Abstract Bayesian inversions followed by estimations of rare event probabilities are often needed to analyze groundwater hazards. Instead of focusing on the posterior distribution of model parameters, the main interest lies then in the distribution of a specific quantity of interest contingent upon...

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Main Authors: Lea Friedli, Niklas Linde
Format: Article
Language:English
Published: Wiley 2024-02-01
Series:Water Resources Research
Subjects:
Online Access:https://doi.org/10.1029/2023WR036610
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author Lea Friedli
Niklas Linde
author_facet Lea Friedli
Niklas Linde
author_sort Lea Friedli
collection DOAJ
description Abstract Bayesian inversions followed by estimations of rare event probabilities are often needed to analyze groundwater hazards. Instead of focusing on the posterior distribution of model parameters, the main interest lies then in the distribution of a specific quantity of interest contingent upon these parameters. To address the associated methodological challenges, we introduce a two‐stage Sequential Monte Carlo approach. In the first stage, it generates particles that approximate the posterior distribution; in the second stage, it employs subset sampling techniques to assess the probability of the rare event of interest. By considering two hydrogeological problems of increasing complexity, we showcase the efficiency and accuracy of the resulting PostRisk‐SMC method for rare event probability estimation related to groundwater hazards. We compare the performance of the PostRisk‐SMC method with a traditional Monte Carlo approach that relies on Markov chain Monte Carlo samples. We showcase that our estimates align with those of the traditional method, but the coefficients of variation are notably lower for the same computational budget when targeting more rare events. Furthermore, we highlight that the PostRisk‐SMC method allows estimating rare event probabilities approaching one in a billion using less than one hundred thousand forward simulations. Even if the presented examples are related to groundwater hazards, the methodology is well‐suited for addressing a wide range of topics in the geosciences and beyond.
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spelling doaj-art-db5c24f65d924c7f9054bb9dfd542b372025-08-20T03:22:26ZengWileyWater Resources Research0043-13971944-79732024-02-01602n/an/a10.1029/2023WR036610Rare Event Probability Estimation for Groundwater Inverse Problems With a Two‐Stage Sequential Monte Carlo ApproachLea Friedli0Niklas Linde1Institute of Earth Sciences University of Lausanne Lausanne SwitzerlandInstitute of Earth Sciences University of Lausanne Lausanne SwitzerlandAbstract Bayesian inversions followed by estimations of rare event probabilities are often needed to analyze groundwater hazards. Instead of focusing on the posterior distribution of model parameters, the main interest lies then in the distribution of a specific quantity of interest contingent upon these parameters. To address the associated methodological challenges, we introduce a two‐stage Sequential Monte Carlo approach. In the first stage, it generates particles that approximate the posterior distribution; in the second stage, it employs subset sampling techniques to assess the probability of the rare event of interest. By considering two hydrogeological problems of increasing complexity, we showcase the efficiency and accuracy of the resulting PostRisk‐SMC method for rare event probability estimation related to groundwater hazards. We compare the performance of the PostRisk‐SMC method with a traditional Monte Carlo approach that relies on Markov chain Monte Carlo samples. We showcase that our estimates align with those of the traditional method, but the coefficients of variation are notably lower for the same computational budget when targeting more rare events. Furthermore, we highlight that the PostRisk‐SMC method allows estimating rare event probabilities approaching one in a billion using less than one hundred thousand forward simulations. Even if the presented examples are related to groundwater hazards, the methodology is well‐suited for addressing a wide range of topics in the geosciences and beyond.https://doi.org/10.1029/2023WR036610inverse theorystatistical methodscontamination breakthroughgroundwater hazard
spellingShingle Lea Friedli
Niklas Linde
Rare Event Probability Estimation for Groundwater Inverse Problems With a Two‐Stage Sequential Monte Carlo Approach
Water Resources Research
inverse theory
statistical methods
contamination breakthrough
groundwater hazard
title Rare Event Probability Estimation for Groundwater Inverse Problems With a Two‐Stage Sequential Monte Carlo Approach
title_full Rare Event Probability Estimation for Groundwater Inverse Problems With a Two‐Stage Sequential Monte Carlo Approach
title_fullStr Rare Event Probability Estimation for Groundwater Inverse Problems With a Two‐Stage Sequential Monte Carlo Approach
title_full_unstemmed Rare Event Probability Estimation for Groundwater Inverse Problems With a Two‐Stage Sequential Monte Carlo Approach
title_short Rare Event Probability Estimation for Groundwater Inverse Problems With a Two‐Stage Sequential Monte Carlo Approach
title_sort rare event probability estimation for groundwater inverse problems with a two stage sequential monte carlo approach
topic inverse theory
statistical methods
contamination breakthrough
groundwater hazard
url https://doi.org/10.1029/2023WR036610
work_keys_str_mv AT leafriedli rareeventprobabilityestimationforgroundwaterinverseproblemswithatwostagesequentialmontecarloapproach
AT niklaslinde rareeventprobabilityestimationforgroundwaterinverseproblemswithatwostagesequentialmontecarloapproach