rMIPPP_cond_mark: Generate a Marked Poisson point process (conditional on mark)
In sppmix: Modeling Spatial Poisson and Related Point Processes

Description Usage Arguments Details Value Author(s) References See Also Examples

This function generates realizations (point patterns) from a given Marked IPPP via conditioning of the joint intensity surface on its marked component. See details for the choice of models for the mark distribution. For each mark value we obtain a ground process. There processes are standard IPPP (unmarked) with mixture intensity surfaces. The mark distribution is responsible for the number of events in the point pattern.

For examples see

http://faculty.missouri.edu/~micheasa/sppmix/sppmix_all_examples.html#rMIPPP_cond_mark

rMIPPP_cond_mark(lambda = 500, params = c(0.5, 0.5),
  mark_distr_choice = 0, truncate = FALSE, discrete_mark = TRUE,
  win = owin(c(-3, 3), c(-3, 3)), bigwin, open_new_window = FALSE,
  grayscale = FALSE, show_plots = TRUE)

`lambda`	Average number of mark values observed over the window. This is the total number of points observed (on the average).
`params`	Parameters for the mark distribution. The value depends on the `mark_distr_choice` parameter, e.g., `params` is a vector of probabilities if the mark distribution is discrete (`mark_distr_choice=0`).
`mark_distr_choice`	A number indicating which mark distribution to use. In the discrete mark case, the mark distribution is discrete over the marks `1:length(params)` with corresponding probabilities in `params`. The continuous mark case has not been implemented yet.
`truncate`	Logical variable indicating whether or not we normalize the densities of the mixture components to have all their mass within the window defined in the window `win`. This affects the mixture model for the intensity surface of the ground process.
`discrete_mark`	Logical flag indicating whether the mark is discrete or not. Default is TRUE. For continuous marks set this to FALSE.
`win`	Object of type `owin` defining the window of observation.
`bigwin`	Object of type `owin`. If supplied, this will be the window of observation, even if the pattern is generated over `win`. Useful if we do not truncate (`truncate=FALSE`) and we want better presentation of the generated MIPPP.
`open_new_window`	Open a new window for a plot.
`grayscale`	Logical to request plots in grayscale.
`show_plots`	Logical variable requesting to produce exploratory plots of the Marked IPPP intensity surface and generated point pattern for each mark.

For discrete marks, we assume that the joint intensity function of a marked point pattern N=[s,m] with n events is of the form:

intensity(s,m)=lambda*M(m|theta1)*g(s(m)|theta2(m))

where m denotes a mark and s=s(m) a location with mark m, lambda a parameter with the interpretation as the average number of events over the window of observation, and M the mark distribution and g the ground intensity are proper densities.

In order to simulate from this Marked IPPP we first simulate the number of events and their marks from an IPPP with intensity lambda*M(m|theta1), and then generate the ground intensities for each mark. Marks are assumed to be independnet of each other and the mixture parameters describing each ground process are also assumed to be independent of each other.

The continuous mark case will be implemented in future releases.

See Micheas (2014) for more details on Marked IPPP models via conditioning arguments.

A list containing the following components:

`groundsurfs`	A list of `intensity_surface` objects containing the surfaces of the ground processes (one for each discrete mark value).
`groundPPs`	A list of `ppp` objects containing the locations of the ground processes (one for each discrete mark value).
`genMPP`	The generated point pattern as an object of class `ppp` and `sppmix`. The member `$marks` contains the marks at each of the generated locations.
`mark_distr_choice`	The choice of mark distribution. Same as the supplied parameter.
`params`	The default or supplied parameter `params`.

Sakis Micheas

Hierarchical Bayesian Modeling of Marked Non-Homogeneous Poisson Processes with finite mixtures and inclusion of covariate information. Micheas, A.C. (2014). Journal of Applied Statistics, 41, 12, 2596-2615, DOI: 10.1080/02664763.2014.922167.

plotmix_2d

# Create a marked point pattern; use randomization and 2 discrete uniform
# marks (default values)
newMPP=rMIPPP_cond_mark(bigwin = spatstat::owin(c(-10,10),c(-10,10)))
newMPP$params
plot(newMPP$genMPP, showmarks=TRUE)+add_title("Marked Poisson point pattern",
 n=newMPP$genMPP$n, nmarks=2)
plotmix_2d(newMPP$groundsurfs[[1]], newMPP$groundPPs[[1]])+ add_title(
 "Poisson point pattern for mark 1", n=newMPP$genMPP$n, m=newMPP$groundsurfs[[1]]$m)
plotmix_2d(newMPP$groundsurfs[[2]], newMPP$groundPPs[[2]])+ add_title(
 "Poisson point pattern for mark 2", n=newMPP$genMPP$n, m=newMPP$groundsurfs[[2]]$m)