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2019 | OriginalPaper | Chapter

Uncertainty Quantification of Complex System Models: Bayesian Analysis

Authors : Jasper A. Vrugt, Elias C. Massoud

Published in: Handbook of Hydrometeorological Ensemble Forecasting

Publisher: Springer Berlin Heidelberg

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Abstract

This chapter summarizes the main elements of Bayesian probability theory to help reconcile dynamic environmental system models with observations, including prediction in space (interpolation), prediction in time (forecasting), assimilation of data, and inference of the model parameters. Special attention is given to the treatment of parameter uncertainty (first-order approximations and Bayesian intervals), the prior distribution, the formulation of the likelihood function (using first-principles), the marginal likelihood, and sampling techniques used to estimate the posterior target distribution. This includes rejection sampling, importance sampling, and recent developments in Markov chain Monte Carlo simulation to sample efficiently complex and/or high-dimensional target distributions, including limits of acceptability. We illustrate the application of Bayes’ theorem and inference using three illustrative examples involving the flow and storage of water in the surface and subsurface. At least some level of calibration of these models is required to match their output with observations of system behavior and response. Algorithmic recipes of the different methods are provided to simplify implementation and use of Bayesian analysis.

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Title: Uncertainty Quantification of Complex System Models: Bayesian Analysis
Authors: Jasper A. Vrugt
Elias C. Massoud
Publisher: Springer Berlin Heidelberg
Book: Handbook of Hydrometeorological Ensemble Forecasting
Print ISBN: 978-3-642-39924-4

Electronic ISBN: 978-3-642-39925-1

Copyright Year: 2019
DOI: https://doi.org/10.1007/978-3-642-39925-1_27