Generate interaction point patterns

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Description

Generate one (or several) realisation(s) of the inhibition or contagious process in a region S x T.

Usage

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 rinter(npoints,s.region,t.region,hs="step",gs="min",thetas=0,
 deltas,ht="step",gt="min",thetat=1,deltat,recent="all",nsim=1,
 discrete.time=FALSE,replace=FALSE,inhibition=TRUE,...)

Arguments

npoints

number of points to simulate.

s.region

two-column matrix specifying polygonal region containing all data locations. If s.region is missing, the unit square is considered.

t.region

vector containing the minimum and maximum values of the time interval. If t.region is missing, the interval [0,1] is considered.

hs, ht

function which depends on the distance between points and theta. Can be chosen among "step" and "gaussian" or can refer to a user defined function which only depend on d, theta, and delta (see details). If inhibition=TRUE, h is monotone, increasing, and must tend to 1 when the distance tends to infinity. 0 <= h(d,theta) <= 1. Otherwise, h is monotone, decreasing, and must tend to 1 when the distance tends to 0.

thetas, thetat

Parameters of hs and ht functions.

deltas, deltat

Spatial and temporal distance of inhibition.

gs, gt

Compute the probability of acceptance of a new point from hs or ht and recent. Must be choosen among "min", "max" and "prod".

recent

If “all” consider all previous events. If is an integer, say N, consider only the N most recent events.

nsim

number of simulations to generate. Default is 1.

discrete.time

if TRUE, times belong to N, otherwise belong to R^+.

replace

Logical. If TRUE allows times repeat.

inhibition

Logical. If TRUE, an inhibition process is generated. Otherwise, it is a contagious process.

...

Additional parameters if hs and ht are defined by the user.

Value

A list containing:

xyt

matrix (or list of matrices if nsim>1) containing the points (x,y,t) of the simulated point pattern. xyt (or any element of the list if nsim>1) is an object of the class stpp.

s.region, t.region

parameters passed in argument.

Author(s)

Edith Gabriel <edith.gabriel@univ-avignon.fr>, Peter J Diggle.

See Also

plot.stpp, animation and stan for plotting space-time point patterns.

Examples

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# simple inhibition process
inh1 = rinter(npoints=200,thetas=0,deltas=0.05,thetat=0,deltat=0.001,
inhibition=TRUE)
## Not run: stan(inh1$xyt)

# inhibition process using hs and ht defined by the user
hs = function(d,theta,delta,mus=0.1)
{
 res=NULL
 a=(1-theta)/mus
 b=theta-a*delta
 for(i in 1:length(d))
	{	
	if (d[i]<=delta) res=c(res,theta)
	if (d[i]>(delta+mus)) res=c(res,1)
	if (d[i]>delta & d[i]<=(delta+mus)) res=c(res,a*d[i]+b)
	}
 return(res)
}
ht = function(d,theta,delta,mut=0.3)
{
 res=NULL
 a=(1-theta)/mut
 b=theta-a*delta
 for(i in 1:length(d))
	{	
	if (d[i]<=delta) res=c(res,theta)
	if (d[i]>(delta+mut)) res=c(res,1)
	if (d[i]>delta & d[i]<=(delta+mut)) res=c(res,a*d[i]+b)
	}
 return(res)
}
d=seq(0,1,length=100)
plot(d,hs(d,theta=0.2,delta=0.1,mus=0.1),xlab="",ylab="",type="l",
ylim=c(0,1),lwd=2,las=1)
lines(d,ht(d,theta=0.1,delta=0.05,mut=0.3),col=2,lwd=2)
legend("bottomright",col=1:2,lty=1,lwd=2,legend=c(expression(h[s]),
expression(h[t])),bty="n",cex=2)

inh2 = rinter(npoints=100, hs=hs, gs="min", thetas=0.2, deltas=0.1, 
ht=ht, gt="min", thetat=0.1, deltat=0.05, inhibition=TRUE)
## Not run: animation(inh2$xyt, runtime=15, cex=0.8)

# simple contagious process for given spatial and temporal regions
data(northcumbria)
cont1 = rinter(npoints=250, s.region=northcumbria, t.region=c(1,200), 
thetas=0, deltas=5000, thetat=0, deltat=10, recent=1, inhibition=FALSE)

## Not run: 
plot(cont1$xyt,pch=19,s.region=cont1$s.region,mark=TRUE,mark.col=4)

## End(Not run)