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Uncertainty

Uncertainty. “God does not play dice” Einstein “The more we know about our universe, the more difficult it becomes to believe in determinism.” Prigogine, 1977 Nobel Prize What remains is: Quantifiable probability with uncertainty. Situation. All data includes some uncertainty

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Uncertainty

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  1. Uncertainty • “God does not play dice” • Einstein • “The more we know about our universe, the more difficult it becomes to believe in determinism.” • Prigogine, 1977 Nobel Prize • What remains is: • Quantifiable probability with uncertainty

  2. Situation • All data includes some uncertainty • The uncertainty is usually not documented • Most modeling methods do not provide uncertainty outputs

  3. Solution? • Estimate the uncertainty in the measured values and the predictor variables • Use “Monte Carlo” methods: • Inject “noise” into the input data • Create the model • Repeat 1 and 2 over and over • Find the distribution of the model outputs • i.e. the parameters and statistical measures • E.g. coefficients, R2, p values, etc.

  4. Douglas-Fir sample data Create the Model Noise Model “Parameters” Precip Extract Prediction To Points Text File Attributes To Raster Noise

  5. Estimating Uncertainty • Field data • Distribution of x,y values • Measurements • Predictor layers • Interpolated • Remotely Sensed

  6. Down Sampling

  7. Original raster at 10 meter resolution (DEM)

  8. Down sampled to 90 meters (each pixel is the mean of the pixels it overlaps with)

  9. Mean Raster

  10. Standard deviation of the pixels that each pixel was derived from.

  11. Additional Error • What was the distribution of the contents of each pixel when it was sampled? What’s in a Pixel? Cracknell, 2010

  12. Pixel Sampling • Each pixel represents an area that is: • Elliptical • Larger than the pixels dimensions

  13. Point-Spread Function • AVHRR

  14. Resampling

  15. Approach? • Estimate the standard deviation of the original scene that the pixels represent • Use this estimate to create predictor rasters that we down sample for the modeling

  16. Original raster at 10 meter resolution (DEM)

  17. Original raster with noise injection

  18. Monte Carlo Error Injection • Create the model with the “mean raster” • Inject normally distributed random “error” into the predictors • Recreate the model • Repeat 2 & 3 saving results • Create distribution of the parameters and performance measures (R2, AIC, AUC, etc.)

  19. Interpolated Predictors • Many predictors are interpolated from point-source data • Kriging provides a standard deviation raster as one of it’s output (these are rarely available) • By injecting error into the point data and recreating the interpolated surface, we can characterize the error in it. • We can also use this to characterize the error’s impact on the model as above

  20. "GSENM" by User:Axcordion - http://en.wikipedia.org/wiki/File:GSENM.JPG. Licensed under CC BY-SA 3.0 via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:GSENM.jpg#mediaviewer/File:GSENM.jpg

  21. http://www.planetware.com/tourist-attractions/utah-usut.htm

  22. Zion http://www.planetware.com/tourist-attractions/utah-usut.htm

  23. Where was the data collected? • On flat spots • Near roads • Often at airports! • The data is not representative of our entire landscape

  24. We’re Missing Data! Interpolated Raster Canyon

  25. Approach • If you created the interpolated surface: • Use Monte Carlo methods to repeatedly recreate the interpolated surface to see the effect of missing data • Regardless: • Estimate the variability that was missed • Maybe from a DEM? • Use this as an uncertainty raster?

  26. Lab This Week • Characterizing the uncertainty in Remotely Sensed data

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