Description Usage Arguments Details Value Author(s) References See Also Examples
This function generates realizations (point patterns) from a given Marked IPPP or a generated one. See details for the choice of models for the mark distribution. The location (ground) process is a standard IPPP (unmarked) with mixture intensity surface, and 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_loc
1 2 3 4 5 
surf 
An object of type 
locPP 
The ground IPPP (locations of the events). If missing then these
are generated using a call to 
gammas 
For discrete marks ( 
r 
Radius used to define the
neighborhood system. Any two locations
within this distance are considered
neighbors. If missing, we randomly select
the radius using the generated (ground) point
pattern over the window parameter 
hyper 
Hyperparameter for the distribution of gamma. 
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 
Object of type 
bigwin 
Object of type 
discrete_mark 
Logical flag indicating whether the mark is discrete or not. Default is TRUE. For continuous marks set this to FALSE. 
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. 
LL 
Length of the side of the square grid. The larger this value is, the better the picture resolution. 
L 
Number of iterations. Required when sampling from the mark model conditional on locations. 
mark_distr_choice 
A number indicating which
mark distribution to use. Currently we have
only one choice in the discrete mark case, which is essentialy a Markov random field (MRF)
over the window. See details for more on the mark model currently used. For continuous marks,
we have two choices, Gaussian random field (GRF) for

GRFmu 
This is the mean of the
Gaussian random field. Only stationarity
is currently supported (i.e., 
df 
Degrees of freedom (an integer) for the
chisquare random field when 
nu, theta, sig 
Additional arguments passed to the

We assume that the joint distribution of a
marked point pattern N=[s,m(s)]
with n
events is of the form:
p(N)=lambda^n*exp(lambda)/(n!)*f(all stheta1)*g(all mtheta2(s),all s)
where s
denotes a location and m=m(s)
a mark value at that location, lambda a parameter
with the interpretation as the average number of points
over the window of observation, and f
, g
are proper densities.
In order to simulate from this Marked IPPP
we first simulate the number of events
and their locations from an IPPP with
mixture intensity surface lambda*f(stheta1)
(e.g.,
using rsppmix
), and then generate
the mark at that location s
.
In the discrete mark case, the mark is modeled using
a mixture distribution of Dirac measures on
the marks with the probability q(m,s)
of observing a
specific mark value m
depending on the current location
s
and the marks of its neighbors. Since
we have a window of observation, any point in there
can potentially be marked, which leads to q(m,s)
being
a field. In particular, the probability q(m,s)
is analogous to
exp(gammas_(j)*(sum over all neighbors of s of their marks minus m squared))
and when we fit the MIPPP model, our goal
is to estimate the parameters gammas
.
Note that if all gammas
are zero then
we fall back to a discrete uniform mark distribution.
The neighborhood system is controlled by
r
and is crucial in this case. Small values
tend to produce probability fields with concentrated
masses about observed events of the process,
whereas, large neighborhoods allow us to borrow
strength across locations and result in much smoother
probability fields.
In the continuous case the mark is generated from
a (typically stationary) Gaussian process or chisquared random process,
e.g., using function rGRF
.
See Micheas (2014) for more details on Marked IPPP models via conditioning arguments.
A list containing the following components:
surf 
The generated or supplied intensity surface object 
gammas 
The generated or supplied parameters 
genMPP 
The generated point pattern as an object of class 
r 
The generated or supplied parameter 
prob_fields 
In the continuous mark case this is the realization of the random field (as an image 
prob_field_params 
A list of the parameters used to create the continuous valued mark fields. Returned only if 
Sakis Micheas
Hierarchical Bayesian Modeling of Marked NonHomogeneous Poisson Processes with finite mixtures and inclusion of covariate information. Micheas, A.C. (2014). Journal of Applied Statistics, 41, 12, 25962615, DOI: 10.1080/02664763.2014.922167.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15  # Create a marked point pattern; use randomization and discrete marks (default values)
newMPP=rMIPPP_cond_loc()
plot(newMPP$surf,main="True IPPP intensity surface for the locations")
newMPP$gammas
newMPP$genMPP
newMPP$r
print(table(newMPP$genMPP$marks))
#we can reproduce the random field plots anytime using the following call
plot_MPP_fields(newMPP$genMPP,newMPP$gammas,newMPP$r)
#Now generate continuous marks according to a Gaussian process
newMPP=rMIPPP_cond_loc(discrete_mark = FALSE)
plot(newMPP$surf,main="True IPPP intensity surface for the locations")
#now the marks are taken from a chisquare field
newMPP=rMIPPP_cond_loc(mark_distr_choice=1, discrete_mark = FALSE)
plot(newMPP$surf,main="True IPPP intensity surface for the locations")

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