1. Some thoughts on density surface updating 1.Major Updates every X years: refitting models (perhaps new kinds of models) to accumulated data over large areas. 2.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. b.Must accommodate any kind of density surface model (including stratified density estimates).

2. 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.)

3. 3 Updating a cell

4. 4 Multi-cell Example

5. 5

6. 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.

7. Another Example 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. Survey Estimate Current Density Updated, Unsmoothed Updated, Smoothed

8. 1. Smoothing Current Density (Example at single location)

9. Current Density Smoothed Smoothing: Periodic smooth (interpolate current estimates) Take account of uncertainty in fitting and reflect in fit. (not shown above)

10. 2. Updating with New Survey Estimate (Example: single location, Month 2) Current Smoothed Estimate at Month=2

11. Updated estimate 2. Updating with New Survey Estimate (Example: single location, Month 2) New Survey Estimate

12. 2. Updating with New Survey Estimate (Example: single location, Month 2) Updated Smooth

13. Another update and Smooth

14. And One More...

15. All Together

16. 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.

17. Multiple Locations etc....

18. 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.)