Spatial models integrating two survey platforms

David L Miller
CREEM, University of St Andrews
converged.yt

National Oceanic and Atmospheric Administration
Visual and Passive Acoustic Data Integration Modeling Workshop
Woods Hole, Massachusetts
15 September 2015




This talk

Case study:
Common loons in Rhode Island

A common loon (Gavia immer)

Photo by jackanapes on flickr (CC BY-NC-ND)

OSAMP

Rhode Island Surveys

How do we integrate this data?

Considerations

Density surface models

(Spatial models that account for detectability)


(…and more)

\(\geq 2\)-stage models




Hedley and Buckland (2004). Miller et al (2013).

Detectability

Distance sampling - line transects

Code for animation at https://gist.github.com/dill/2b0c120d5484d338d8ef

Detection functions

Detection functions

\(\mathbb{P} \left[ \text{animal detected } \vert \text{ animal at distance } y\right]\)

Integrate out distance: \[ \hat{p}_i = \frac{1}{w} \int_0^w g(y; \boldsymbol{\hat{\theta}}, z_i) \text{d}y \]

or…

\(p=1\)

Availability

Availability correction


Effort

Data setup

Gavia immer from PhyloPic.

Effort

Overlap

Overlap

Spatially explicit models

Spatial model

\[ \mathbb{E}(\hat{n}_j) = A_j\exp \left\{ \beta_0 + \sum_k f_k(z_{jk}) \right\} \]



Variance estimation

Uncertainty propagation

Conclusions

Conclusions

Acknowledgements

Thanks!

Slides available at
converged.yt

Course at Duke in October:
nicholas.duke.edu/del/distance

References