A Bayesian Approach to the Estimation of Parameters and Their Interdependencies in Environmental Modeling

Christopher G. Albert*, Ulrich Callies, Udo von Toussaint

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We present a case study for Bayesian analysis and proper representation of distributions and dependence among parameters when calibrating process-oriented environmental models. A simple water quality model for the Elbe River (Germany) is referred to as an example, but the approach is applicable to a wide range of environmental models with time-series output. Model parameters are estimated by Bayesian inference via Markov Chain Monte Carlo (MCMC) sampling. While the best-fit solution matches usual least-squares model calibration (with a penalty term for excessive parameter values), the Bayesian approach has the advantage of yielding a joint probability distribution for parameters. This posterior distribution encompasses all possible parameter combinations that produce a simulation output that fits observed data within measurement and modeling uncertainty. Bayesian inference further permits the introduction of prior knowledge, e.g., positivity of certain parameters. The estimated distribution shows to which extent model parameters are controlled by observations through the process of inference, highlighting issues that cannot be settled unless more information becomes available. An interactive interface enables tracking for how ranges of parameter values that are consistent with observations change during the process of a step-by-step assignment of fixed parameter values. Based on an initial analysis of the posterior via an undirected Gaussian graphical model, a directed Bayesian network (BN) is constructed. The BN transparently conveys information on the interdependence of parameters after calibration. Finally, a strategy to reduce the number of expensive model runs in MCMC sampling for the presented purpose is introduced based on a newly developed variant of delayed acceptance sampling with a Gaussian process surrogate and linear dimensionality reduction to support function-valued outputs.

Original languageEnglish
Article number231
JournalEntropy
Volume24
Issue number2
DOIs
Publication statusPublished - Feb 2022

Keywords

  • Bayesian network
  • Delayed acceptance
  • Markov chain Monte Carlo
  • Model calibration
  • Overparameterization
  • Posterior parameter dependence

ASJC Scopus subject areas

  • Information Systems
  • Mathematical Physics
  • Physics and Astronomy (miscellaneous)
  • Electrical and Electronic Engineering

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