Power-posterior implicit sampling for efficient Bayesian experimental design: Application to contaminant source identification in groundwater flow
Abstract
Model-based Bayesian optimal experimental design aims to enhance Bayesian learning of a parameter of interest by identifying experimental set-ups that maximize the informativeness of data. The informativeness of the data is assessed through its expected effect on the uncertainty associated with the parameter of interest, as characterized by the posterior probability distribution. To measure this value, we adopt the Shannon expected information gain, a design criterion that is particularly effective for nonlinear models, although it is computationally expensive to evaluate with classical sampling methods and prone to numerical underflow. To reduce the estimation cost, we reformulate the Shannon expected information gain as an integral of expected log-likelihoods along a power-posterior path connecting the prior and posterior distributions. The proposed method relies on marginal-based sampling and determines the numerical sampling requirements needed to achieve a prescribed estimation accuracy. Realizations from each transitional distribution are drawn implicitly using linear and random mappings. We examine computational complexity using a one-dimensional Darcy flow problem and then demonstrate the effectiveness of the method for optimal sensor placement with an application to contaminant source identification in a heterogeneous porous medium governed by a time-dependent advection-diffusion differential equation in a two-dimensional physical domain.
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BibTeX
@misc{dia2026powerposterior,
title = {{Power-posterior implicit sampling for efficient Bayesian experimental design: Application to contaminant source identification in groundwater flow}},
author = {Ben Mansour Dia and Joakim Beck and Anamika Pandey and Oliver Dorn},
howpublished = {HAL},
year = {2026},
month = oct,
url = {https://hal.science/hal-05837498v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Power-posterior implicit sampling for efficient Bayesian experimental design: Application to contaminant source identification in groundwater flow
AU - Ben Mansour Dia
AU - Joakim Beck
AU - Anamika Pandey
AU - Oliver Dorn
PY - 2026
DA - 2026/10/23
PB - HAL
UR - https://hal.science/hal-05837498v1
AB - Model-based Bayesian optimal experimental design aims to enhance Bayesian learning of a parameter of interest by identifying experimental set-ups that maximize the informativeness of data. The informativeness of the data is assessed through its expected effect on the uncertainty associated with the parameter of interest, as characterized by the posterior probability distribution. To measure this value, we adopt the Shannon expected information gain, a design criterion that is particularly effective for nonlinear models, although it is computationally expensive to evaluate with classical sampling methods and prone to numerical underflow. To reduce the estimation cost, we reformulate the Shannon expected information gain as an integral of expected log-likelihoods along a power-posterior path connecting the prior and posterior distributions. The proposed method relies on marginal-based sampling and determines the numerical sampling requirements needed to achieve a prescribed estimation accuracy. Realizations from each transitional distribution are drawn implicitly using linear and random mappings. We examine computational complexity using a one-dimensional Darcy flow problem and then demonstrate the effectiveness of the method for optimal sensor placement with an application to contaminant source identification in a heterogeneous porous medium governed by a time-dependent advection-diffusion differential equation in a two-dimensional physical domain.
ER -