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| Titel |
A flexible Bayesian assessment for the expected impact of data on prediction confidence for optimal sampling designs |
| VerfasserIn |
Philipp Leube, Andreas Geiges, Wolfgang Nowak |
| Konferenz |
EGU General Assembly 2010
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 12 (2010) |
| Datensatznummer |
250042596
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| Zusammenfassung |
| Incorporating hydrogeological data, such as head and tracer data, into stochastic models of
subsurface flow and transport helps to reduce prediction uncertainty. Considering limited
financial resources available for the data acquisition campaign, information needs towards the
prediction goal should be satisfied in a efficient and task-specific manner. For finding the best
one among a set of design candidates, an objective function is commonly evaluated, which
measures the expected impact of data on prediction confidence, prior to their collection. An
appropriate approach to this task should be stochastically rigorous, master non-linear
dependencies between data, parameters and model predictions, and allow for a wide
variety of different data types. Existing methods fail to fulfill all these requirements
simultaneously.
For this reason, we introduce a new method, denoted as CLUE (Cross-bred Likelihood
Uncertainty Estimator), that derives the essential distributions and measures of
data utility within a generalized, flexible and accurate framework. The method
makes use of Bayesian GLUE (Generalized Likelihood Uncertainty Estimator) and
extends it to an optimal design method by marginalizing over the yet unknown
data values. Operating in a purely Bayesian Monte-Carlo framework, CLUE is a
strictly formal information processing scheme free of linearizations. It provides
full flexibility associated with the type of measurements (linear, non-linear, direct,
indirect) and accounts for almost arbitrary sources of uncertainty (e.g. heterogeneity,
geostatistical assumptions, boundary conditions, model concepts) via stochastic simulation
and Bayesian model averaging. This helps to minimize the strength and impact of
possible subjective prior assumptions, that would be hard to defend prior to data
collection. Our study focuses on evaluating two different uncertainty measures: (i)
expected conditional variance and (ii) expected relative entropy of a given prediction
goal.
The applicability and advantages are shown in a synthetic example. Therefor, we consider a
contaminant source, posing a threat on a drinking water well in an aquifer. Furthermore, we
assume uncertainty in geostatistical parameters, boundary conditions and hydraulic gradient.
The two mentioned measures evaluate the sensitivity of (1) general prediction confidence and
(2) exceedance probability of a legal regulatory threshold value on sampling locations. |
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