How can model structure uncertainty (i.e. unobserved end-members) and observation errors be represented explicitly?

1. 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

2. Groundwater mixing analysis
Endmember 1Endmember 2

3. Groundwater Mixing Analysis
Andreas Scheidegger

4. Errors! Where do they come from?
Or is your
model wrong?
Ah,
observation
errors!

5. Analytics is difficult. Fieldwork is messy…
Observations model
But any other distribution
could be used.
Andreas Scheidegger

6. If I had perfect measurements, would I still expect errors?
Model structure error
?
Andreas Scheidegger

7. If I had perfect measurements, would I still expect errors?
Model structure error
Model unknown endmember explicitly:
?
Andreas Scheidegger

8. Bayesian Inference
Andreas Scheidegger

9. Bayesian Inference
Easy to implement in Stan, Jags, WinBugs, PyMC3, Turing.jl, …
Andreas Scheidegger

10. Results Hardwald
10
Residual endmember

11. 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