Point processes

GeoStatsProcesses.BinomialProcess — Type

BinomialProcess(n)

A Binomial point process with n points.

source

# geometry of interest
box = Box((0, 0), (100, 100))

# Binomial process
proc = BinomialProcess(1000)

# sample point patterns
pset = rand(proc, box, 2)

fig = Mke.Figure(size = (800, 400))
viz(fig[1,1], box)
viz!(fig[1,1], pset[1], color = :black)
viz(fig[1,2], box)
viz!(fig[1,2], pset[2], color = :black)
fig

GeoStatsProcesses.PoissonProcess — Type

PoissonProcess(λ)

A Poisson process with intensity λ. For a homogeneous process, define λ as a constant real value, while for an inhomogeneous process, define λ as a function or vector of values. If λ is a vector, it is assumed that the process is associated with a Domain with the same number of elements as λ.

source

# geometry of interest
box = Box((0, 0), (100, 100))

# intensity function
λ(p) = sum(to(p))^2 / 10000

# homogeneous process
proc₁ = PoissonProcess(0.5)

# inhomogeneous process
proc₂ = PoissonProcess(λ)

# sample point patterns
pset₁ = rand(proc₁, box)
pset₂ = rand(proc₂, box)

fig = Mke.Figure(size = (800, 400))
viz(fig[1,1], box)
viz!(fig[1,1], pset₁, color = :black)
viz(fig[1,2], box)
viz!(fig[1,2], pset₂, color = :black)
fig

GeoStatsProcesses.InhibitionProcess — Type

InhibitionProcess(δ)

An inhibition point process with minimum distance δ.

source

# geometry of interest
box = Box((0, 0), (100, 100))

# inhibition process
proc = InhibitionProcess(2.0)

# sample point pattern
pset = rand(proc, box, 2)

fig = Mke.Figure(size = (800, 400))
viz(fig[1,1], box)
viz!(fig[1,1], pset[1], color = :black)
viz(fig[1,2], box)
viz!(fig[1,2], pset[2], color = :black)
fig

GeoStatsProcesses.ClusterProcess — Type

ClusterProcess(proc, ofun)

A cluster process with parent process proc and offsprings generated with ofun. It is a function that takes a parent point and returns a point pattern from another point process.

ClusterProcess(proc, offs, gfun)

Alternatively, specify the parent process proc, the offspring process offs and the geometry function gfun. It is a function that takes a parent point and returns a geometry or domain for the offspring process.

source

# geometry of interest
box = Box((0, 0), (5, 5))

# Matérn process
proc₁ = ClusterProcess(
  PoissonProcess(1),
  PoissonProcess(1000),
  p -> Ball(p, 0.2)
)

# inhomogeneous parent and offspring processes
proc₂ = ClusterProcess(
  PoissonProcess(p -> 0.1 * sum(to(p) .^ 2)),
  p -> rand(PoissonProcess(x -> 5000 * sum((x - p).^2)), Ball(p, 0.5))
)

# sample point patterns
pset₁ = rand(proc₁, box)
pset₂ = rand(proc₂, box)

fig = Mke.Figure(size = (800, 400))
viz(fig[1,1], box)
viz!(fig[1,1], pset₁, color = :black)
viz(fig[1,2], box)
viz!(fig[1,2], pset₂, color = :black)
fig