introduction to spatial point process models for distance ... · model.spde(dset, cv) g(s) cv(s); s...
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![Page 1: Introduction to Spatial Point Process Models for Distance ... · model.spde(dset, cv) g(s) cv(s); s 2 make.model(fml, cv) See INLA f() model.detfun(type) log p(z)!type = "halfnormal"](https://reader033.vdocuments.us/reader033/viewer/2022050521/5fa45a3256de8f5358197153/html5/thumbnails/1.jpg)
Introduction to Spatial Point Process Models for Distance Sampling Data: using the package iDistance
Introduction to Spatial Point Process Models forDistance Sampling Data:
using the package iDistance
March 18, 2016
![Page 2: Introduction to Spatial Point Process Models for Distance ... · model.spde(dset, cv) g(s) cv(s); s 2 make.model(fml, cv) See INLA f() model.detfun(type) log p(z)!type = "halfnormal"](https://reader033.vdocuments.us/reader033/viewer/2022050521/5fa45a3256de8f5358197153/html5/thumbnails/2.jpg)
Introduction to Spatial Point Process Models for Distance Sampling Data: using the package iDistance
Section
subsection
Practical 2: Introduction
![Page 3: Introduction to Spatial Point Process Models for Distance ... · model.spde(dset, cv) g(s) cv(s); s 2 make.model(fml, cv) See INLA f() model.detfun(type) log p(z)!type = "halfnormal"](https://reader033.vdocuments.us/reader033/viewer/2022050521/5fa45a3256de8f5358197153/html5/thumbnails/3.jpg)
Introduction to Spatial Point Process Models for Distance Sampling Data: using the package iDistance
Section
subsection
Practical 2: Introduction
![Page 4: Introduction to Spatial Point Process Models for Distance ... · model.spde(dset, cv) g(s) cv(s); s 2 make.model(fml, cv) See INLA f() model.detfun(type) log p(z)!type = "halfnormal"](https://reader033.vdocuments.us/reader033/viewer/2022050521/5fa45a3256de8f5358197153/html5/thumbnails/4.jpg)
Introduction to Spatial Point Process Models for Distance Sampling Data: using the package iDistance
Section
subsection
Practical 2: Introduction
Recall
π(Y|Λ) = exp
(|Ω| −
∫Ω
Λ(s) ds
) NY(Ω)∏i=1
Λ(si )
Our task is to design log Λ in terms of
Detection functionsAnimal/group intensityPoissibly other bits
![Page 5: Introduction to Spatial Point Process Models for Distance ... · model.spde(dset, cv) g(s) cv(s); s 2 make.model(fml, cv) See INLA f() model.detfun(type) log p(z)!type = "halfnormal"](https://reader033.vdocuments.us/reader033/viewer/2022050521/5fa45a3256de8f5358197153/html5/thumbnails/5.jpg)
Introduction to Spatial Point Process Models for Distance Sampling Data: using the package iDistance
Section
subsection
Practical 2: Introduction
model log Λ
model.intercept() cmodel.fixed(cv) β · cv(s), s ∈ Ωmodel.spde(dset, cv) g(s) · cv(s), s ∈ Ωmake.model(fml, cv) See INLA f()
model.detfun(type) log p(z)→ type = "halfnormal" −1
2βz2
→ type = "exponential" −βz→ type = "hazard" log[1− exp(−( z
σ )−b)]
After designing the components, we build a joint model:
jmdl = join(model.intercept(), model.spde(dset))
![Page 6: Introduction to Spatial Point Process Models for Distance ... · model.spde(dset, cv) g(s) cv(s); s 2 make.model(fml, cv) See INLA f() model.detfun(type) log p(z)!type = "halfnormal"](https://reader033.vdocuments.us/reader033/viewer/2022050521/5fa45a3256de8f5358197153/html5/thumbnails/6.jpg)
Introduction to Spatial Point Process Models for Distance Sampling Data: using the package iDistance
Section
subsection
Practical 2: Introduction
![Page 7: Introduction to Spatial Point Process Models for Distance ... · model.spde(dset, cv) g(s) cv(s); s 2 make.model(fml, cv) See INLA f() model.detfun(type) log p(z)!type = "halfnormal"](https://reader033.vdocuments.us/reader033/viewer/2022050521/5fa45a3256de8f5358197153/html5/thumbnails/7.jpg)
Introduction to Spatial Point Process Models for Distance Sampling Data: using the package iDistance
Section
subsection
Practical 2: Introduction
![Page 8: Introduction to Spatial Point Process Models for Distance ... · model.spde(dset, cv) g(s) cv(s); s 2 make.model(fml, cv) See INLA f() model.detfun(type) log p(z)!type = "halfnormal"](https://reader033.vdocuments.us/reader033/viewer/2022050521/5fa45a3256de8f5358197153/html5/thumbnails/8.jpg)
Introduction to Spatial Point Process Models for Distance Sampling Data: using the package iDistance
Section
subsection
Practical 2: Introduction
![Page 9: Introduction to Spatial Point Process Models for Distance ... · model.spde(dset, cv) g(s) cv(s); s 2 make.model(fml, cv) See INLA f() model.detfun(type) log p(z)!type = "halfnormal"](https://reader033.vdocuments.us/reader033/viewer/2022050521/5fa45a3256de8f5358197153/html5/thumbnails/9.jpg)
Introduction to Spatial Point Process Models for Distance Sampling Data: using the package iDistance
Section
subsection
Practical 2: Introduction
The main method for running inference is idst()
idst() is a wrapper for INLA!
Argument What for?
model Put in your model here, e.g. jmdl
data Your data set, e.g. weeds
ips A data.frame of integration pointspredict A list defining what and where to predict (optional)
verbose Tell INLA to be verbose... Pass these arguments on to INLA
![Page 10: Introduction to Spatial Point Process Models for Distance ... · model.spde(dset, cv) g(s) cv(s); s 2 make.model(fml, cv) See INLA f() model.detfun(type) log p(z)!type = "halfnormal"](https://reader033.vdocuments.us/reader033/viewer/2022050521/5fa45a3256de8f5358197153/html5/thumbnails/10.jpg)
Introduction to Spatial Point Process Models for Distance Sampling Data: using the package iDistance
Section
subsection
Practical 2: Introduction
After running idst, check out your results!
Function What for?
summary() Check if your INLA output makes senseevaluate() Obtain intensity at some locationmarginal() Posterior of a single effect or parameterplot.spatial() A spatial plot of your resultsplot.detfun() Plot the detection function