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Bayesian end-member mixing analysis with explicit
consideration of unobserved end-members
and measurement uncertainty
Andreas Scheidegger
Andrea Popp
Christian Möck
Matthias Brennwald
EGU − April 10th, 2019
Groundwater mixing analysis
Endmember 1Endmember 2
Groundwater Mixing Analysis
Andreas Scheidegger
Errors! Where do they come from?
Or is your
model wrong?
Ah,
observation
errors!
Analytics is difficult. Fieldwork is messy…
Observations model
But any other distribution
could be used.
Andreas Scheidegger
If I had perfect measurements, would I still expect errors?
Model structure error
?
Andreas Scheidegger
If I had perfect measurements, would I still expect errors?
Model structure error
Model unknown endmember explicitly:
?
Andreas Scheidegger
Bayesian Inference
Andreas Scheidegger
Bayesian Inference
Easy to implement in Stan, Jags, WinBugs, PyMC3, Turing.jl, …
Andreas Scheidegger
Results Hardwald
10
Residual endmember
Conclusions
Measurement errors:
 Observation model
Structural model
limitations:
 Residual end-
member as error source
• Protects from over-confidence
• Combines expert knowledge
• Allows to learn from model errors
• Can guide future experiments
Making assumption explicit:
Source of all pictograms: thenounproject.com Thanks!Andreas Scheidegger

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Bayesian End-Member Mixing Model