LGCPs - Plot sampling
David Borchers and Finn Lindgren
Generated on 2024-04-30
Source:vignettes/articles/2d_lgcp_plotsampling.Rmd
2d_lgcp_plotsampling.Rmd
Introduction
This practical demonstrates use of the samplers
argument
in lgcp
, which you need to use when you have observed
points from only a sample of plots in the survey region.
Get the data
data(gorillas, package = "inlabru")
This dataset is a list (see help(gorillas)
for details.
Extract the the objects you need from the list, for convenience:
nests <- gorillas$nests
mesh <- gorillas$mesh
boundary <- gorillas$boundary
gcov <- gorillas$gcov
The gorillas
data also contains a plot sample subset
which covers 60% of the survey region.
sample <- gorillas$plotsample
plotdets <- ggplot() +
gg(boundary) +
gg(sample$plots) +
gg(sample$nests, pch = "+", cex = 4, color = "red") +
geom_text(aes(label = sample$counts$count, x = sample$counts$x, y = sample$counts$y)) +
labs(x = "Easting", y = "Northing")
plot(plotdets)
On this plot survey, only points within the rectangles are detected, but it is also informative to plot all the points here (which if it was a real plot survey you could not do, because you would not have seen them all).
plotwithall <- ggplot() +
gg(boundary) +
gg(sample$plots) +
gg(nests, pch = "+", cex = 4, color = "blue") +
geom_text(aes(label = sample$counts$count, x = sample$counts$x, y = sample$counts$y)) +
gg(sample$nests, pch = "+", cex = 4, color = "red") +
labs(x = "Easting", y = "Northing")
plot(plotwithall)
Inference
The observed nest locations are in the SpatialPointsDataFrame
sample$nests
, and the plots are in the
SpatialPolygonsDataFrame sample$plots
. Again, we are using
the following SPDE setup:
matern <- inla.spde2.pcmatern(mesh,
prior.sigma = c(0.1, 0.01),
prior.range = c(0.05, 0.01)
)
Fit an LGCP model with SPDE only to these data by using the
samplers=
argument of the function
lgcp( )
:
cmp <- coordinates ~ my.spde(coordinates, model = matern)
fit <- lgcp(cmp, sample$nests, samplers = sample$plots, domain = list(coordinates = mesh))
Plot the density surface from your fitted model
pxl <- fm_pixels(mesh, mask = boundary, format = "sp")
lambda.sample <- predict(fit, pxl, ~ exp(my.spde + Intercept))
lambda.sample.plot <- ggplot() +
gg(lambda.sample) +
gg(sample$plots) +
gg(boundary, col = "yellow")
lambda.sample.plot
Estimate the integrated intensity lambda. We compute both the overall integrated intensity, representative of an imagined new realisation of the point process, and the conditional expectation that takes the actually observed nests into account, by recognising that we have complete information in the surveyed plots.
Lambda <- predict(fit, fm_int(mesh, boundary), ~ sum(weight * exp(my.spde + Intercept)))
Lambda.empirical <- predict(
fit,
rbind(
cbind(fm_int(mesh, boundary), data.frame(all = TRUE)),
cbind(fm_int(mesh, sample$plots), data.frame(all = FALSE))
),
~ (sum(weight * exp(my.spde + Intercept) * all) -
sum(weight * exp(my.spde + Intercept) * !all) +
nrow(sample$nests))
)
rbind(
Lambda,
Lambda.empirical
)
Fit the same model to the full dataset (the points in
gorillas$nests
), or get your previous fit, if you kept it.
Plot the intensity surface and estimate the integrated intensity
fit.all <- lgcp(cmp, gorillas$nests,
samplers = gorillas$boundary,
domain = list(coordinates = mesh)
)
lambda.all <- predict(fit.all, pxl, ~ exp(my.spde + Intercept))
Lambda.all <- predict(fit.all, fm_int(mesh, boundary), ~ sum(weight * exp(my.spde + Intercept)))
Your plot should look like this:
The values Lambda.empirical
, Lambda
, and
Lambda.all
should be close to each other if the plot
samples gave sufficient information for the overall prediction:
rbind(
Lambda,
Lambda.empirical,
Lambda.all,
Lambda.all.empirical =
c(nrow(gorillas$nests), 0, rep(nrow(gorillas$nests), 3), rep(NA, 3))
)
#> mean sd q0.025 q0.5 q0.975 median mean.mc_std_err
#> 1 656.7662 53.14265 565.7431 650.7158 770.1802 650.7158 5.314265
#> 2 648.0718 39.92723 581.4243 644.3614 741.8768 644.3614 3.992723
#> 3 672.3603 25.24791 628.0101 671.5833 720.5667 671.5833 2.524791
#> 4 647.0000 0.00000 647.0000 647.0000 647.0000 NA NA
#> sd.mc_std_err
#> 1 4.038598
#> 2 4.140080
#> 3 1.677823
#> 4 NA
Now, let’s compare the results
library(patchwork)
lambda.sample.plot + lambda.all.plot +
plot_layout(guides = "collect") &
theme(legend.position = "left") &
scale_fill_continuous(limits = range(c(0, 340)))
Do you understand the reason for the differences in the posteriors of the abundance estimates?