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Some thoughts on density surface updating. Major Updates every X years: refitting models (perhaps new kinds of models) to accumulated data over large areas.

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some thoughts on density surface updating
Some thoughts on density surface updating
  • Major Updates every X years: refitting models (perhaps new kinds of models) to accumulated data over large areas.
  • Minor Updates as and when new (reliable) survey estimates become available: Use new estimates to modify existing surfaces locally (spatially and temporally).

a. Should be quick and easy.

    • Must accommodate any kind of density surface

model (including stratified density estimates).

bayesian update
Bayesian Update?
  • Problem 1: How accommodate any kind of density surface model? (Models could have few/no common parameters.)
  • Solution 1: Update densities cell-by-cell rather than parameters.
    • Assume (say) lognormal distribution of density.
    • Need variance-covariance matrix of cell densities.
    • (End product is a weighted average.)
bayesian update1
Bayesian Update?
  • Problem 2: How get smooth edges?
  • Solution 2: Smooth via weights decaying with distance from edge
    • Easy to smooth; not so easy to find the best amount of smoothing.
another example
Another Example

Current Density

Survey Estimate

  • Survey Estimates update current surface at single point in time.
  • Two-stage updating:
    • Bayesian Update within survey region.
    • Smoothing across survey region boundary.
  • Current surface and Updated surface apply for whole season (quarter), then jump/drop suddenly to that for next season.

Updated, Unsmoothed

Updated, Smoothed

current density smoothed
Current Density Smoothed
  • Smoothing:
  • Periodic smooth (interpolate current estimates)
  • Take account of uncertainty in fitting and reflect in fit.
  • (not shown above)
2 updating with new survey estimate example single location month 2
2. Updating with New Survey Estimate (Example: single location, Month 2)

Current Smoothed Estimate at Month=2

2 updating with new survey estimate example single location month 21
2. Updating with New Survey Estimate (Example: single location, Month 2)

New Survey Estimate

Updated estimate

cumulative effect
Cumulative Effect
  • Smooth Temporal Updating:
    • Degree of Smoothness: more flexible with more data.
    • Effect of update decays with temporal “distance”.
    • Uncertainty in new smooth (not shown above) updated smoothly in time too.
3 spatio temporal interaction
3. Spatio-Temporal Interaction
  • How similar in space should temporal effects be? Constraining temporal smooths closer together to be more similar will prevent inconsistent temporal trends at locations near each other. (Unclear in advance how necessary this will prove to be.)