bootcor_restr {highriskzone}

Bootstrap correction to obtain desired failure probability

Description

Simulation-based iterative procedure to correct for possible bias with respect to the failure probability alpha

Usage

bootcor_restr(
  ppdata,
  cutoff,
  numit = 100,
  tol = 0.001,
  nxprob = 0.1,
  hole = NULL,
  obsprobimage = NULL,
  intens = NULL,
  covmatrix = NULL,
  simulate = "intens",
  radiusClust = NULL,
  clustering = 5,
  verbose = TRUE
)

Arguments

ppdata

Observed spatial point process of class ppp.

cutoff

Desired failure probability alpha, which is the probability of having unobserved events outside the high-risk zone.

numit

Number of iterations to perform (per tested value for cutoff). Default value is 1000.

tol

Tolerance: acceptable difference between the desired failure probability and the fraction of high-risk zones not covering all events. Default value is 0.02.

nxprob

Probability of having unobserved events. Default value is 0.1.

hole

(optional) an object of class owin representing a region inside the observation window of the ppdata where no observations were possible.

obsprobimage

(optional) an object of class im giving the observation probabilities inside the observation window. Ranges of the coordinates must equal those of ppdata. Only used if obsprobs is not given.

intens

(optional) estimated intensity of the observed process (object of class "im", see density.ppp). If not given, it will be estimated.

covmatrix

(optional) Covariance matrix of the kernel of a normal distribution, only meaningful if no intensity is given. If not given, it will be estimated.

simulate

The type of simulation, can be one of "thinning", "intens" or "clintens"

radiusClust

(optional) radius of the circles around the parent points in which the cluster points are located. Only used for simulate = "clintens".

clustering

a value >= 1 which describes the amount of clustering; the adjusted estimated intensity of the observed pattern is divided by this value; it also is the parameter of the Poisson distribution for the number of points per cluster. Only used for simulate = "clintens".

verbose

logical. Should information on tested values/progress be printed?

Details

For a desired failure probability alpha, the corresponding parameter which is to use when determining a high-risk zone is found in an iterative procedure. The simulation procedure is the same as in eval_method. In every iteration, the number of high-risk zones with at least one unobserved event located outside is compared with the desired failure probability. If necessary, the value of cutoff is increased or decreased. The final value alphastar can than be used in det_hrz.

The function offers the possibility to take into account so-called restriction areas. This is relevant in situations where the observed point pattern ppdata is incomplete. If it is known that no observations can be made in a certain area (for example because of water expanses), this can be accounted for by integrating a hole in the observation window. The shape and location of the hole is given by hole. Holes are part of the resulting high-risk zone. Another approach consists in weighting the observed events with their reciprocal observation probability when estimating the intensity. To do so, the observation probability can be specified by using obsprobsimage (an image of the observation probability). Note that the observation probability may vary in space.

For further information, see Mahling (2013), Appendix A (References).

If there are no restriction areas in the observation window, bootcor can be used instead.

Value

An object of class bootcorr, which consists of a list of the final value for alpha (alphastar) and a data.frame course containing information on the simulation course, e.g. the tested values.

References

Monia Mahling, Michael H?hle & Helmut K?chenhoff (2013), Determining high-risk zones for unexploded World War II bombs by using point process methodology. Journal of the Royal Statistical Society, Series C 62(2), 181-199.

Monia Mahling (2013), Determining high-risk zones by using spatial point process methodology. Ph.D. thesis, Cuvillier Verlag G?ttingen, available online: http://edoc.ub.uni-muenchen.de/15886/ Chapter 6 and Appendix A

See Also

det_hrz, eval_method, bootcor

Examples

data(craterA)
set.seed(4321)
# define restriction area
restrwin <- spatstat.geom::owin(xrange = craterA$window$xrange, 
                          yrange = craterA$window$yrange,
                          poly = list(x = c(1500, 1500, 2000, 2000), 
                                      y = c(2000, 1500, 1500, 2000)))

# create image of observation probability (30% inside restriction area)
wim <- spatstat.geom::as.im(craterA$window, value = 1)
rim <- spatstat.geom::as.im(restrwin, xy = list(x = wim$xcol, y = wim$yrow))
rim$v[is.na(rim$v)] <- 0
oim1 <- spatstat.geom::eval.im(wim - 0.7 * rim)

## Not run: 
# perform bootstrap correction
bc1 <- bootcor_restr(ppdata=craterA, cutoff=0.4, numit=100, tol=0.02, obsprobimage=oim1, nxprob=0.1)
bc1
summary(bc1)
plot(bc1)

# determine high-risk zone by weighting the observations
hrzi1 <- det_hrz_restr(ppdata=craterA, type = "intens", criterion = "indirect",
 cutoff = bc1$alphastar, hole=NULL, obsprobs=NULL, obsprobimage=oim1, nxprob = 0.1)

# perform bootstrap correction
set.seed(4321)
bc2 <- bootcor_restr(ppdata=craterA, cutoff=0.4, numit=100, tol=0.02, hole=restrwin, nxprob=0.1)
bc2
summary(bc2)
plot(bc2)

# determine high-risk zone by accounting for a hole
hrzi2 <- det_hrz_restr(ppdata=craterA, type = "intens", criterion = "indirect",
 cutoff = bc2$alphastar, hole=restrwin, obsprobs=NULL, obsprobimage=NULL, nxprob = 0.1)

## End(Not run)