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Dealing with uncertainty

This informational guide from the GEOPRIV motivational series explores the concepts of uncertainty and confidence in measurements, emphasizing their importance in dealing with stochastic processes. It covers the significance of confidence intervals, error bars, and common misinterpretations in scientific literature. The document also provides practical shortcuts for effectively managing uncertainty, including methods for converting complex data into useful estimates. Understanding the interplay between uncertainty and confidence is crucial for accurate location determination and informed decision-making.

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Dealing with uncertainty

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  1. Dealing with uncertainty From the GEOPRIV motivational series

  2. Drafts • draft-thomson-geopriv-uncertainty-08 • What uncertainty (and confidence) mean and are good for • A bunch of shortcuts for dealing with uncertainty • Intended status: Informational • draft-thomson-geopriv-confidence-04 • A small addition to PIDF-LO • Intended status: Proposed Standard

  3. Uncertainty draft-thomson-geopriv-uncertainty-08

  4. Statistics Refresher: Confidence Intervals • It’s common to describe measurements of stochastic processes (i.e., random $#!^) as confidence intervals • Graphs with the following are very common in scientific literature: The average/median is here 95% of the time, it’s between here… and here.

  5. Terminology is surprisingly important • Accuracy = • fuzzy, feel good term • qualitative, no numbers, use it when talking in the abstract • Uncertainty = • quantitative, concrete, supported with numbers • useless without confidence • Confidence = • probabilistic measure for uncertainty • quantitative, concrete, has numbers [0, 1) or [0, 100%) • Combine uncertainty and confidence: • 95% of the time (confidence), the value is between X and Y (uncertainty range)

  6. Lies, damned lies, and… • The error bars hide a lot of details • The observed probability distribution is rarely perfectly normal • Outliers can be irrelevant, or interesting, but they disappear • Other interesting points like mean, median, variance, all go • But that’s OK, because it’s hard to process more detailed information

  7. RFC 5491 defines error bars in 3D (and 2D)

  8. Still masking greater complexity Ellipse/ellipsoid are pretty good for capturing the product of least squares or Kalman filters Particle filters are much harder to capture …draft-hoene-geopriv-bli http://here.com/37.7873082,-122.4066945,16,0,0,gray.day

  9. Mo’ data, mo’ troubles • Even the simplified information can be too much • There are a bunch of things you can’t do safely/easily • Most amount to the fact that you can’t invent information you don’t have • E.g., can’t scale uncertainty without information loss • Some applications require very little information • A point • Maybe a circle/sphere radius (so they can report “accuracy”) • Is this location estimate “the same” as this other one • So how do we get there? • draft-thomson-geopriv-uncertainty contains a bunch of cheats

  10. Cheats • Convert to point: • A simple method for calculating centroids of all the RFC 5491 shapes • Not so easy for polygons, but a robust approximation method provided • Get single number for uncertainty:; • Two cheats: convert to circle • Use point calculation and find furthest point • Scale uncertainty based on probability distribution assumptions

  11. Scaling • Not always a good idea • Relies on assumptions • Big mistakes possible • Scaling down is risky, scaling up is basically impossible • Unless you have some extra information. Reported (95%) PDF Scaled down (assumed to be ~68%, but closer to 5%)

  12. Confidence draft-thomson-geopriv-confidence-04

  13. PIDF-LO assumes 95% confidence • …and doesn’t allow for divergence from this number • That’s a problem for implementations that are required to convert • Many existing systems produce estimates at other values • Conversion without sufficient knowledge requires assumptions • Assumptions cause data loss and errors

  14. Impossibilities • Sometimes 95% is unattainable • A >5% absolute error rate can happen • Maybe you are operating from a source that it just that bad • No alteration of the uncertainty value (other than to have it encompass the entire planet) can compensate for the errors • e.g., Location determination based on a data set that is completely, irretrievably wrong 13.4% of the time • Confidence cannot be 86.6% or higher

  15. Scaling hint • Help with scaling by having an optional hint on PDF shape • Normal – scale up or down safely • Rectangular – scale down safely • Unknown – scale at own risk

  16. Backwards compatibility • None • Intentionally – confidence changes everything • …but it does more damage when you solve for backward compatibility • Scaling = bad • Alternative is no location information at all • Only real solution is to admonish not to use confidence unless you are reasonably sure that the recipient will understand

  17. There Is Hope Adopt

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