Tkp: Compute the vector T^k*p

In latticeDensity: Density Estimation and Nonparametric Regression on Irregular Regions

Description

TranMat is the transition matrix of the random walk on the lattice. By multiplying by the probability density p at time t, you get the probability density at time t+1. Thus, to get the probability density after k steps, pk, compute pk = Tkp1. This application of finite Markov processes is described in Barry and McIntyre (2011).

Usage

Tkp(TranMat, k, p)

Arguments

TranMat	Transition matrix returned by makeTmatrix.
k	The number of steps in the diffusion.
p	A numerical vector of length equal to the number of nodes, of initial probabilities.

Value

A vector of probabilities.

Author(s)

Ronald P. Barry

References

Ronald P. Barry, Julie McIntyre. Estimating animal densities and home range in regions with irregular boundaries and holes: A lattice-based alternative to the kernel density estimator. Ecological Modelling 222 (2011) 1666-1672.

Examples

plot.new()
data(polygon1)
nodeFillingOutput <- nodeFilling(poly=polygon1, node_spacing=0.015)
formLatticeOutput <- formLattice(nodeFillingOutput)
Pointdata <- splancs::csr(polygon1,75)
Pointdata <- Pointdata[Pointdata[,1]<0.5, ]
init_prob <- addObservations(formLatticeOutput, Pointdata)
TranMat <- makeTmatrix(formLatticeOutput, M = 0.5, sparse=TRUE)
p10 <- Tkp(TranMat, k=10, p=init_prob$init_prob)
head(cbind(init_prob$init_prob, p10))

latticeDensity documentation built on April 18, 2021, 5:06 p.m.