Analysing spatial point patterns in R - CSIRO

23.4 Generic algorithm for minimum contrast 147
1.0485493 0.0997963
Derived parameters of log-Gaussian Cox process ($modelpar):
sigma2 alpha mu
1.0485493 0.0997963 3.6028597
Converged successfully after 145 iterations.
Domain of integration: [ 0 , 0.25 ]
Exponents: p= 2, q= 0.25
The second argument to lgcp.estK gives initial values for the model parameters σ 2 and α.
The result of lgcp.estK is an object of class minconfit (representing a ‘minimum contrast
fit’). There are methods for printing and plotting the fit. Simulation of these models has not
yet been implemented in spatstat.
Estimation can also be based on the pair correlation function:
> fit fit
Minimum contrast fit (object of class minconfit)
Model: log-Gaussian Cox process
Fitted by matching theoretical g function to pcf(redwood)
Parameters fitted by minimum contrast ($par):
sigma2 alpha
1.30244010 0.07011464
Derived parameters of log-Gaussian Cox process ($modelpar):
sigma2 alpha mu
1.30244010 0.07011464 3.47591433
Converged successfully after 83 iterations.
Domain of integration: [ 0.0004883 , 0.25 ]
Exponents: p= 2, q= 0.25
23.4 Generic algorithm for minimum contrast
The command mincontrast is a generic fitting algorithm for the method of minimum contrast.
It can be used in any context where the theoretical function can be computed exactly from the
model parameters. A basic call to mincontrast is:
> mincontrast(observed, theoretical, starpar)
where observed is an object of class "fv" containing the summary function calculated from
the data; theoretical is a function which returns the theoretical value of the summary function
for a given parameter value; and startpar is a vector of initial values of the model parameters.
For details, see the help file for mincontrast.
For the vast majority of point process models, the true K function K θ (r) is not known
analytically in terms of the parameter θ. In principle we could use Monte Carlo simulation
to determine an approximation to K θ (r), for any given θ, by generating a large number of
simulated realisations of the process with parameter θ, computing the estimated K-function for
each realisation, and taking the pointwise sample average. It’s possible to do this in spatstat
using the generic algorithm mincontrast. Details are not given here as it is rather fiddly at
present, and will change soon.
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