Determining high-risk zones by using spatial point process methodology

Description

The package highriskzone provides tools to determine and evaluate high-risk zones of unobserved events by using point process methodology.

Author(s)

Heidi Seibold Heidi.Seibold@campus.lmu.de, Monia Mahling monia.mahling@stat.uni-muenchen.de Sebastian Linne Sebastian.Linne@campus.lmu.de Felix Guenther felix.guenther@stat.uni-muenchen.de Maintainer: Felix Guenther felix.guenther@stat.uni-muenchen.de

References

Monia Mahling, Michael Hoehle & Helmut Kuechenhoff (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 Goettingen, available online: http://edoc.ub.uni-muenchen.de/15886/

Heidi Seibold (2012), Determining high risk zones using point process methodology - Realization by building an R package. Bachelor Thesis, Ludwig Maximilian University of Munich.

See Also

spatstat-package

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(
  ppdata,
  cutoff,
  numit = 1000,
  tol = 0.02,
  nxprob = 0.1,
  intens = NULL,
  covmatrix = NULL,
  simulate = "intens",
  radiusClust = NULL,
  clustering = 5,
  verbose = TRUE
)

Arguments

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.

If there are restriction areas in the observation window, use bootcor_restr 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

See Also

det_hrz, eval_method, bootcor_restr

Examples

## Not run: 
data(craterB)
set.seed(4321)

bc <- bootcor(ppdata=craterB, cutoff=0.2, numit=100, tol=0.02, nxprob=0.1)
bc
summary(bc)
plot(bc)


hrzbc <- det_hrz(craterB, type = "intens", criterion = "indirect", 
cutoff = bc$alphastar, nxprob = 0.1)

## End(Not run)

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

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)

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

bootcorr(
  ppdata,
  cutoff,
  numit = 1000,
  tol = 0.02,
  nxprob = 0.1,
  intens = NULL,
  covmatrix = NULL,
  simulate = "intens",
  radiusClust = NULL,
  clustering = 5,
  verbose = TRUE
)

Arguments

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.

If there are restriction areas in the observation window, use bootcor_restr 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

See Also

det_hrz, eval_method, bootcor_restr

Examples

## Not run: 
data(craterB)
set.seed(4321)

bc <- bootcor(ppdata=craterB, cutoff=0.2, numit=100, tol=0.02, nxprob=0.1)
bc
summary(bc)
plot(bc)


hrzbc <- det_hrz(craterB, type = "intens", criterion = "indirect", 
cutoff = bc$alphastar, nxprob = 0.1)

## End(Not run)

Checks the arguments of det_hrz

Description

For each argument it is checked if it is of a correct value or class.

Usage

check_det_hrz_input(
  ppdata,
  type,
  criterion,
  cutoff,
  distancemap,
  intens,
  nxprob,
  covmatrix
)

Arguments

See Also

det_hrz

Checks the arguments of det_hrz_restr

Description

For each argument it is checked if it is of a correct value or class.

Usage

check_det_hrz_restr_input(
  ppdata,
  type,
  criterion,
  cutoff,
  hole,
  integratehole,
  obsprobs,
  obsprobimage,
  distancemap,
  intens,
  nxprob,
  covmatrix,
  returnintens
)

Arguments

Bomb crater Point Pattern

Description

Bomb crater Point Pattern

Usage

data(craterA)

Format

An object of class "ppp" representing a point pattern of bomb craters. The Cartesian coordinates are in meters. See ppp.object for details of the format of a point pattern object.

Bomb crater Point Pattern

Description

Bomb crater Point Pattern

Usage

data(craterB)

Format

An object of class "ppp" representing a point pattern of bomb craters. The Cartesian coordinates are in meters. See ppp.object for details of the format of a point pattern object.

calculation of alpha (failure probability), when having the threshold c

Description

This function is used for the intensity-based method. It determines the probability to have at least one unobserved event outside the high-risk zone. A Poisson distribution is used for the number of unobserved events in a certain area or field. Used in functions det_threshold, det_thresholdfromarea.

Usage

det_alpha(intens, threshold, nxprob = 0.1)

Arguments

Value

value of alpha

Determination of failure probability within evaluation area

Description

Determination of failure probability within evaluation area

Usage

det_alpha_eval_ar(intens, eval_ar, threshold, nxprob = 0.1)

Arguments

Calculation of the area of the high-risk zone.

Description

This function is used for the intensity-based method. Calculation of the area of the high-risk zone given the observation window, the intensity matrix and the threshold c. Used in function det_thresholdfromarea.

Usage

det_area(win, intensmatrix, threshold)

Arguments

Value

A numerical value giving the area of the high-risk zone.

See Also

owin, area.owin

Calculation of the area of the high-risk zone.

Description

This function is used for the intensity-based method with a hole restriction area. Calculation of the area of the high-risk zone given the observation window, the intensity matrix, the threshold c and a hole. Used in function det_thresholdfromarea_hole.

Usage

det_area_hole(win, intensmatrix, threshold, hole, integratehole = TRUE)

Arguments

Value

A numerical value giving the area of the high-risk zone.

See Also

owin, area.owin

Estimation of width of a guard region given an estimated highriskzone

Description

det_guard_width determines the necessary width of a guard region in which the existence of additional observed bomb craters could change a intensity based estimated highriskzone within the evaluation area of interest. Within the evaluation area, the high risk zone consists of all points at which the estimated intensity of unexploded bombs exceeds a certain, specified or estimated threshold c. At a given point s, the intensity of unexploded bombs is given by the sum of all evaluated bivariate normal kernels centered at the observed bomb craters multiplied by a constant nxprob/1-nxprob. If the estimated intensity of unexploaded bombs is zero at a point at the boarder of the evaluation area an additional observation outside the area could lift the intensity only above the determined threshold if the distance to the boarder is small enough so that the density of the normal kernel (which is centered at the additional observation) is bigger than the threshold at the boarder (assuming that the estimated kernel doesn't change due to the additional observation). The function returns the biggest distance in which it is possible that the density of the bivariate normal kernel of the intensity of the supplied highriskzone exceeds thresh_const times the threshold of the highriskzone. If thresh_const is set to 1, the guard region is the smallest region with constant width around the evaluation area in which a single additional observation could (but not necessarily does) increase the highriskzone within the evaluation area at a point at the boarder if the intensity of unexploaded bombs was zero at this point before. If the intensity was >0 at a point at the boarder of the evaluation area, or more than 1 additional observations are found nearby outside of the evaluation area, the highriskzone within the evaluation area could already expand by addditional observations with a bigger distance from the boarder. This can be considered by setting thresh_const < 1, which intuitively means that 1/thresh_const crater observation at the same point could expand the highriskzone within the evaluation area in the direction of the additional observations, or that a point the boarder becomes part of the highriskzone by the observation of a single additional crater if the intensity at this point was thresh_cont times the highriskzone threshold based on all crater observations within the evaluation area.

Usage

det_guard_width(highriskzone, thresh_const = 0.5)

Arguments

Details

For more infos on the construction of guard zones see Mahling (2013, Appendix B, Approach 2)

Value

The constant width of the guard region.

Examples

## change npixel to 1000 to obtain nicer plots
spatstat.geom::spatstat.options(npixel=100)
data(craterA)
# reduce number of observations for faster computation
thin.craterA <- craterA[1:50]
hrzi1 <- det_hrz(thin.craterA, type = "intens", criterion = "area", cutoff = 100000, nxprob = 0.1)
det_guard_width(hrzi1, thresh_const = .25)

Determination of the high-risk zone.

Description

det_hrz determines the high-risk zone through the method of fixed radius (type = "dist" and criterion = "direct"), the quantile-based method (type = "dist" and criterion = "area"/"indirect") and the intensity-based method (type = "intens").

Usage

det_hrz(
  ppdata,
  type,
  criterion,
  cutoff,
  distancemap = NULL,
  intens = NULL,
  nxprob = 0.1,
  covmatrix = NULL
)

Arguments

Details

There are different methods implemented to determine a high-risk zone.

Method of fixed radius

In this method, the high-risk zone is determined by drawing a circle around each observed event with a fixed radius. This method will be used when type = "dist" and criterion = "direct". cutoff then is the radius.

Quantile-based method

This method is a development of the above. Here the radius is not fixed. It uses the distance of every observed event to the nearest other event, which is calculated by the nearest-neighbour distance. The radius is assessed by the p-quantile of the empirical distribution function of the nearest-neighbour distance. This method will be used when type = "dist" and criterion = "indirect" or "area". If criterion = "indirect", then cutoff is the quantile that should be used. If criterion = "area" then cutoff is the area that the high-risk zone has to have at the end and from that the quantile/the radii are determined. When the calculation is done via the area, it can not really be classified to the quantile-based method. It is rather a third "distance-based" method.

Intensity-based method

The first step of this method is to estimate the intensity of the observed events. Based on the estimated intensity and the specified probability of unobserved bombs nxprob it is possible to estimate the intensity of unobserved/unexploded bombs. The high-risk zone is then the area in which the estimated intensity of unexploded bombs exceeds a certain value. This value is called threshold c. The method will be used when type = "intens". There are three different ways to construct a high-risk zone:

1. Fixing the threshold c: criterion = "direct"

2. Fixing the area of the high-risk zone: criterion = "area"

3. Fixing the failure probability alpha, which is the probability of having unobserved events outside the high-risk zone: criterion = "indirect" Here, the point process is assumed to be an inhomogeneous Poisson process.

For further information see Mahling et al. (2013) (References).

If there are restriction areas in the observation window, use det_hrz_restr instead. For estimation of intensity based highrikszones with a bigger observation area than area of interest (evaluation area) use det_hrz_eval_ar.

Value

An object of class "highriskzone", which is a list of

References

Monia Mahling, Michael Hoehle & Helmut Kuechenhoff (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 Goettingen, available online: http://edoc.ub.uni-muenchen.de/15886/

See Also

distmap, eval.im, owin, eval_method, det_hrz_restr

Examples

 data(craterA)
## change npixel to 1000 to obtain nicer plots
spatstat.geom::spatstat.options(npixel=100)
## type: dist
hrzd1 <- det_hrz(craterA, type = "dist", criterion = "area", cutoff = 1000000, nxprob = 0.1)
hrzd2 <- det_hrz(craterA, type = "dist", criterion = "indirect", cutoff = 0.9, nxprob = 0.1)
hrzd3 <- det_hrz(craterA, type = "dist", criterion = "direct", cutoff = 100, nxprob = 0.1)

op <- par(mfrow = c(2, 2))
plot(craterA)
plot(hrzd1, zonecol = 2, win = craterA$window, plotwindow = TRUE)
plot(hrzd2, zonecol = 3,  win = craterA$window, plotwindow = TRUE)
plot(hrzd3, zonecol = 4,  win = craterA$window, plotwindow = TRUE)
par(op)

## Not run: 
# or first calculate the distancemap and use it:
distm <- distmap(craterA)
hrzd <- det_hrz(craterA, type = "dist", criterion = "direct", cutoff = 100,
                distancemap = distm, nxprob = 0.1)

## End(Not run)                
## type: intens 
# reduce number of observations for faster computation
thin.craterA <- craterA[1:10]
hrzi1 <- det_hrz(thin.craterA, type = "intens", criterion = "area", cutoff = 100000, nxprob = 0.1)
plot(hrzi1)
plot(thin.craterA, add = TRUE)
plot(thin.craterA$window, add = TRUE)
## Not run: 
hrzi2 <- det_hrz(craterA, type = "intens", criterion = "indirect", cutoff = 0.1, nxprob = 0.1)
hrzi3 <- det_hrz(craterA, type = "intens", criterion = "direct", cutoff = 0.0001, nxprob = 0.1)
plot(hrzi2)
plot(hrzi3)

## End(Not run)
                 
## More detailed examples on http://highriskzone.r-forge.r-project.org/

Determination of high-risk zone on smaller area of interest (evaluation area) than observation area.

Description

det_hrz_eval_ar determines intensity based highriskzones if bomb crater observations are available for a bigger area than the area of main interest (evaluation area). All observations are used for intensity estimation, the highriskzone is however constructed only in the evaluation area. Either based on specifying a failure probability alpha that indicates the probability of unobserved bombs outside the highriskzone but inside the evaluation area of interest (and not in the overall observation area) (criterion = "indirect"), or by specifying the threshold (maximum intensity of non- exploded bombs outside the) highriskzone directly and intersecting the resulting hrz with the evaluation area (criterion = "direct").

Usage

det_hrz_eval_ar(
  ppdata,
  eval_ar,
  criterion = c("indirect", "direct"),
  cutoff,
  intens = NULL,
  nxprob = 0.1,
  covmatrix = NULL
)

Arguments

Value

An object of class "highriskzone"

Examples

set.seed(12412)
spatstat.geom::spatstat.options(npixel=300)
data(craterB)
# reduce number of observations for faster computation
thin.craterB <- craterB[sample(1:craterB$n, 40)]
# define evaluation area of interest
eval.ar <- spatstat.geom::owin(xrange = c(0, 1900), yrange = c(0, 3400), 
               poly = matrix(c(250,250, 1200,1000,250,1000), byrow = TRUE, ncol = 2))

hrzi1 <- det_hrz_eval_ar(thin.craterB, eval_ar = eval.ar, criterion = "direct",
                        cutoff = 3e-6, nxprob = .2)

plot(hrzi1)
plot(thin.craterB, add = TRUE)
plot(eval.ar, add = TRUE)
plot(craterB$window, add = TRUE)

Determination of the high-risk zone.

Description

det_hrz_restr determines the high-risk zone through the method of fixed radius (type = "dist" and criterion = "direct"), the quantile-based method (type = "dist" and criterion = "area"/"indirect") and the intensity-based method (type = "intens"). Restriction areas can be taken into account.

Usage

det_hrz_restr(
  ppdata,
  type,
  criterion,
  cutoff,
  hole = NULL,
  integratehole = TRUE,
  obsprobs = NULL,
  obsprobimage = NULL,
  distancemap = NULL,
  intens = NULL,
  nxprob = 0.1,
  covmatrix = NULL,
  returnintens = TRUE
)

Arguments

Details

Used in functions eval_method, sim_clintens, sim_intens.
This function contains the same functionalities as det_hrz. In addition, it 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, whereas integratehole is used to state whether the hole is to become part of the resulting high-risk zone. This may also be a reasonable approach if only few observations could be made in a certain area. 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 obsprobs (value of the observation probability for each event) or obsprobsimage (image of the observation probability). Note that the observation probability may vary in space.
If there are no restriction areas in the observation window, det_hrz can be used instead.
Note that for criterion = "area", cutoff specifies the area of the high-risk zone outside the hole. If integratehole = TRUE, the area of the resulting high-risk zone will exceed cutoff.

For further information, Mahling et al. (2013) and Mahling (2013), Chapters 4 and 8 and Appendix A (References).

Value

An object of class "highriskzone", which is a list of

See Also

distmap, eval.im, owin

Examples

set.seed(1211515)
data(craterA)
#change npixel = 100 to 1000 to get a nicer picture
spatstat.geom::spatstat.options(npixel=100)
# reduce number of observations for faster computation
craterA <- craterA[sample(1:craterA$n, 150)]
# define restriction area
restrwin <- spatstat.geom::owin(xrange=craterA$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)
# determine high-risk zone by weighting the observations
hrzi1 <- det_hrz_restr(ppdata=craterA, type = "intens", criterion = "indirect",
                       cutoff = 0.4, hole=NULL, obsprobs=NULL, obsprobimage=oim1, nxprob = 0.1)

# determine high-risk zone by accounting for a hole
hrzi2 <- det_hrz_restr(ppdata=craterA, type = "intens", criterion = "indirect",
                       cutoff = 0.4, hole=restrwin, obsprobs=NULL, obsprobimage=NULL, nxprob = 0.1)

Determination of the area of a high-risk zone using the nearest-neighbour distance.

Description

Used in function det_radius.

Usage

det_nnarea(cutoffval, distancemap, win)

Arguments

Value

A numerical value giving the area of the window.

See Also

eval.im, owin, area.owin

Determination of the intensity for the Neyman Scott simulation.

Description

Used in function sim_nsppp.

Usage

det_nsintens(ppdata, radius)

Arguments

Value

A pixel image (object of class "im"). See density.ppp.

See Also

density.ppp, boundingbox, owin, Hscv

Determination of the intensity for the Neyman-Scott simulation.

Description

Used in function bootcor_restr.

Usage

det_nsintens_restr(ppdata, radius, weights)

Arguments

Value

A pixel image (object of class "im"). See density.ppp.

See Also

density.ppp, boundingbox, owin, Hscv

Determination of the nearest-neighbour distance which results in a high-risk zone with desired area

Description

Used in function det_hrz.

Usage

det_radius(ppdata, distancemap, areahrz, win)

Arguments

Value

A list of

See Also

det_nnarea, quantile, uniroot

Calculation of the threshold c, when having failure probability alpha.

Description

The high-risk zone is the field in which the estimated intensity exceeds the threshold c, which is determined here, having the failure probability alpha. This function is for the intensity-based method. Used in function det_hrz.

Usage

det_threshold(intens, alpha = 1e-05, nxprob = 0.1)

Arguments

Value

value of the threshold c

See Also

det_alpha, uniroot

Determination of necessary threshold to keep alpha in evaluation area

Description

Determination of necessary threshold to keep alpha in evaluation area

Usage

det_threshold_eval_ar(intens, eval_ar, alpha = 1e-05, nxprob = 0.1)

Arguments

Determination of alpha and the threshold c which results in a high-risk zone with desired area.

Description

This function is used for the intensity-based method. Used in function det_hrz.

Usage

det_thresholdfromarea(intens, areahrz, win, nxprob = 0.1)

Arguments

Value

A list of

See Also

det_area, det_alpha

Determination of alpha and the threshold c which results in a high-risk zone with desired area if a hole is present.

Description

This function is used for the intensity-based method. Used in function det_hrz_restr.

Usage

det_thresholdfromarea_rest(
  intens,
  areahrz,
  win,
  nxprob = 0.1,
  hole = hole,
  integratehole = TRUE
)

Arguments

Value

A list of

See Also

det_area, det_alpha

Estimates the intensity of the point pattern.

Description

Estimates the intensity of the point pattern by a kernel method (See density.ppp).

Usage

est_intens(ppdata, covmatrix = NULL, weights = NULL)

Arguments

Value

A list of

See Also

density.ppp, Hscv, eval.im

Examples

data(craterA)
#change npixel = 50 to 1000 to get a nicer picture
spatstat.geom::spatstat.options(npixel=50)
# use only ten observations for fast computation
thin.craterA <- craterA[1:10]
int <- est_intens(thin.craterA)
# Plot estimated intensity
plot(int$intensest, main = "pixel image of intensity")
plot(craterA$window, main = "contour plot of intensity")
contour(int$intensest, add =TRUE)

Estimates the intensity of the point pattern by using the SPDE method from r-INLA.

Description

Estimates the intensity of the point pattern by using the SPDE method from r-INLA.

Usage

est_intens_spde(
  coords,
  win = NULL,
  npixel = 50,
  fine_mesh = FALSE,
  mesh = NULL,
  weights = NULL,
  alpha = 2,
  ...
)

Arguments

Value

A list of

Examples

## Not run: 
data(craterA)
est_spde <- est_intens_spde(coords=craterA)
image.plot(list(x=est_spde$intensest$xcol, y=est_spde$intensest$yrow, 
                z=log(t(est_spde$intensest$v))), main="estimated logarithmic intensity")
points(craterA)

## End(Not run)

Estimates the intensity of the point pattern.

Description

Estimates the intensity of the point pattern by a kernel method (See density.ppp).

Usage

est_intens_weight(ppdata, covmatrix = NULL, weights = NULL)

Arguments

Value

A list of

See Also

density.ppp, Hscv, eval.im

Examples

data(craterA)
#change npixel = 50 to 1000 to get a nicer picture
spatstat.geom::spatstat.options(npixel=50)
# use only ten observations for fast computation
thin.craterA <- craterA[1:10]
# weight first 5 observations twice
weights <- c(rep(2, 5), rep(1, 5))
int <- est_intens_weight(thin.craterA, weights = weights)
plot(int$intensest, main = "pixel image of intensity")
plot(craterA$window, main = "contour plot of intensity")
contour(int$intensest, add =TRUE)

Evaluation of the high-risk zone.

Description

Evaluation of the high-risk zone, which is only possible with simulated or thinned data or if the locations of the unobserved events have been revealed..

Usage

eval_hrz(hrz, unobspp, obspp = NULL)

Arguments

Value

An object of class "hrzeval", which is a list of

See Also

inside.owin, area.owin

Examples

 data(craterB)
 # thin data
 set.seed(100)
 thdata <- thin(craterB, nxprob=0.1)
 
 # determine hrz for the "observed events"
 hrz <- det_hrz(thdata$observed, type = "dist", criterion = "area", cutoff = 1500000, nxprob = 0.1)
 
 # evaluate the hrz
 evaluation <- eval_hrz(hrz = hrz$zone, unobspp = thdata$unobserved, obspp = thdata$observed)
 evaluation$missingfrac
 
 op <- par(mar=c(1, 4, 1, 6) , xpd=TRUE)
 plot(evaluation, hrz = hrz, obspp = thdata$observed, plothrz = TRUE, plotobs = TRUE, 
 insidecol = "magenta", outsidecol = "magenta", obscol = "blue", insidepch = 1, 
 outsidepch = 19, main = "Evaluation visualized")
 legend(2400, 2456.4061, c("observed", "unobs inside", "unobs outside"), 
 col = c("blue", "magenta", "magenta"), yjust=1, pch=c(1, 1, 19), cex=0.8)
 par(op)

Evaluation of the procedures determining the high-risk zone.

Description

Evaluates the performance of the three methods:

• Method of fixed radius

• Quantile-based method

• Intensity-based method

For further details on the methods, see det_hrz or the paper of Mahling et al. (2013)(References).
There are three ways to simulate data for the evaluation.

Usage

eval_method(
  ppdata,
  type,
  criterion,
  cutoff,
  numit = 100,
  nxprob = 0.1,
  distancemap = NULL,
  intens = NULL,
  covmatrix = NULL,
  simulate,
  radiusClust = NULL,
  clustering = 5,
  pbar = TRUE
)

Arguments

Details

The three simulation types are:

Data-based simulation

Here a given data set is used. The data set is thinned as explained below. Note that this method is very different from the others, since it is using the real data.

Simulation of an inhomogeneous Poisson process

Here, an inhomogeneous Poisson process is simulated and then that data is thinned.

Simulation of a Neyman-Scott process

Here a Neyman-Scott process is simulated (see sim_nsppp, rNeymanScott) and this data is then also thinned.

Thinning:
Let X be the spatial point process, which is the location of all events and let Y be a subset of X describing the observed process. The process of unobserved events then is Z = X \ Y , meaning that Z and Y are disjoint and together forming X.
Since Z is not known, in this function an observed or simulated spatial point pattern ppdata is taken as the full pattern (which we denote by X') comprising the observed events Y' as well as the unobserved Z'. Each event in X' is assigned to one of the two processes Y' or Z' by drawing independent Bernoulli random numbers.
The resulting process of observed events Y' is used to determine the high-risk zone. Knowing now the unobserved process, it can be seen how many events are outside and inside the high-risk zone.

type and criterion may be vectors in this function.

Value

A data.frame with variables

See Also

det_hrz, rNeymanScott, thin, sim_nsppp, sim_intens

Examples

## Not run:     
 data(craterB)
 
 # the input values are mainly the same as in det_hrz, so for more example ideas, 
 # see the documentation of det_hrz.
 evalm <- eval_method(craterB, type = c("dist", "intens"), criterion = c("area", "area"), 
                      cutoff = c(1500000, 1500000), nxprob = 0.1, numit = 10, 
                      simulate = "clintens", radiusClust = 300, 
                      clustering = 15, pbar = FALSE)
 evalm_d <- subset(evalm, evalm$Type == "dist")
 evalm_i <- subset(evalm, evalm$Type == "intens")
 
 # pout:  fraction of high-risk zones that leave at least one unobserved event uncovered
 # pmiss:  Mean fraction of unobserved events outside the high-risk zone
 data.frame(pmiss_d = mean(evalm_d$missingfrac),
            pmiss_i = mean(evalm_i$missingfrac),
            pout_d = ( sum(evalm_d$numbermiss > 0) / nrow(evalm_d) ), 
            pout_i = ( sum(evalm_i$numbermiss > 0) / nrow(evalm_i) ))

## End(Not run)

Visualize the bootstrap correction for a high-risk zone.

Description

Plot a visualization of the bootstrap correction for a high-risk zone. The different values tested for alpha are plotted.

Usage

## S3 method for class 'bootcorr'
plot(x, ...)

Arguments

Details

This is the plot method for the class bootcorr.

See Also

plot, print.bootcorr, summary.bootcorr

Plot a high-risk zone

Description

Plot a high-risk zone.

Usage

## S3 method for class 'highriskzone'
plot(
  x,
  ...,
  pattern = NULL,
  win = NULL,
  plotpattern = FALSE,
  plotwindow = FALSE,
  windowcol = "white",
  usegpclib = FALSE,
  zonecol = "grey"
)

Arguments

Details

This is the plot method for the class highriskzone.

See Also

plot, for examples see det_hrz

Visualize the evaluation of a high-risk zone.

Description

Plot a visualization of the evaluation of a high-risk zone. At least the observation window and the unobserved events inside and outside the high-risk zone are plotted.

Usage

## S3 method for class 'hrzeval'
plot(
  x,
  ...,
  hrz = NULL,
  obspp = NULL,
  plothrz = FALSE,
  plotobs = FALSE,
  windowcol = "white",
  insidecol = "blue",
  outsidecol = "red",
  insidepch = 20,
  outsidepch = 19,
  zonecol = "grey",
  obscol = "black",
  obspch = 1
)

Arguments

Details

This is the plot method for the class hrzeval.

See Also

plot, eval_hrz, plot.highriskzone

Print Brief Details of a bootstrap correction for a high-risk zone

Description

Prints a very brief description of the bootstrap correction for a high-risk zone.

Usage

## S3 method for class 'bootcorr'
print(x, ...)

Arguments

Details

A very brief description of the bootstrap correction x for a high-risk zone is printed. This is a method for the generic function print.

See Also

print, summary.bootcorr

Print Brief Details of a high-risk zone

Description

Prints a very brief description of a high-risk zone.

Usage

## S3 method for class 'highriskzone'
print(x, ...)

Arguments

Details

A very brief description of the highriskzone x is printed. This is a method for the generic function print.

See Also

print, summary.highriskzone

Print Brief Details of an evaluation of a high-risk zone

Description

Prints a very brief description of the evaluation of a high-risk zone.

Usage

## S3 method for class 'hrzeval'
print(x, ...)

Arguments

Details

A very brief description of the evaluation x of a high-risk zone is printed. This is a method for the generic function print.

See Also

print, summary.hrzeval

Read data, so it can be used for high-risk zone methodology.

Description

If xwin or ywin is NULL, the observation window will be a rectangular bounding box. Vertices must be listed anticlockwise; no vertex should be repeated. Only needed for data that is not already of class ppp.

Usage

read_pppdata(xppp, yppp, xwin = NULL, ywin = NULL, unitname = NULL)

Arguments

Value

An object of class "ppp" describing a point pattern in the two-dimensional plane.

See Also

ppp, bounding.box.xy, owin

Examples

data(craterA)
windowA <- data.frame(x = craterA$window$bdry[[1]]$x, y = craterA$window$bdry[[1]]$y)
patternA <- data.frame(x = craterA$x, y = craterA$y)
str(patternA)
str(windowA)
crater <- read_pppdata(xppp = patternA$x, yppp = patternA$y, 
                       xwin = windowA$x, ywin = windowA$y)
crater

Simulation on given intensity

Description

Generation of a random point pattern using the inhomogeneous Poisson process (if lambda is not constant) and thinning of this data, to obtain "observed" and "unobserved" events.

Usage

sim_intens(ppdata, intensSim, nxprob)

Arguments

Value

A list of of observed and unobserved point patterns (see thin)

See Also

thin, rpoispp

Generation of a realisation of a Neyman-Scott process

Description

This algorithm generates a realisation of a Neyman-Scott process whose expected number of points equals the number of observations in a given pattern.

Usage

sim_nsppp(ppdata, radius, clustering = 5, thinning = 0)

Arguments

Details

First, the algorithm generates a Poisson point process (see rpoispp for details) of parent points with intensity kappa, which is a pixel image object of class "im" (see im.object).
This pixel image is derived from the observed pattern using density.ppp. The bandwidth is not chosen in advance.
If only a thinned version of the original pattern has been observed, this can be taken into account using the parameter thinning. Usually, not the estimated intensity itself is used for simulating the parent process, but its values are divided by a constant named "clustering".
Second, each parent point is replaced by a random cluster of points, created by calling the function runifdisc. Each cluster consists of a Poisson distributed number of points (with clustering being the expected number of points in each cluster) which are located in a disc of a given radius. These clusters are combined to yield a single point pattern which is then returned as the result.
The estimation of the intensity (on an adequate window) and the simulation of the Neyman-Scott process are performed seperately, so the intensity does not need to be reestimated in every iteration.
The resulting process is a Mat?rn process whose parent process is an inhomogeneous Poisson point process.

Value

The simulated point pattern (an object of class "ppp"). Additionally, some intermediate results of the simulation are returned as attributes of this point pattern: see rNeymanScott.

See Also

rNeymanScott, rThomas, rMatClust

Examples

## Not run:       
 data(craterA)
 data(craterB)
 set.seed(100)
 sim_pp1 <- sim_nsppp(craterA, radius=300, clustering=15, thinning=0.1)
 sim_pp2 <- sim_nsppp(craterB, radius=300, clustering=15, thinning=0.1)
 op <- par(mfrow = c(1, 2))
 plot(sim_pp1, main = "simulated cluster process 1")
 plot(sim_pp2, main = "simulated cluster process 2")
 par(op)
 
## End(Not run)

Simulation of the Neyman-Scott process.

Description

Simulation of the Neyman-Scott process. Only applicable if the intensity was estimated for an appropriately enlarged window. More details in sim_nsppp.

Usage

sim_nsprocess(ppdata, intens, radius, clustering = 5, thinning = 0)

Arguments

Value

The simulated point pattern (an object of class "ppp"). Additionally, some intermediate results of the simulation are returned as attributes of this point pattern: see rNeymanScott.

Summary of a the bootstrap correction for a high-risk zone

Description

Prints a useful summary of the bootstrap correction for a high-risk zone.

Usage

## S3 method for class 'bootcorr'
summary(object, ...)

Arguments

Details

A useful summary of the bootstrap correction x for a high-risk zone is printed. This is a method for the generic function summary.

See Also

summary, print.bootcorr, plot.bootcorr

Summary of a high-risk zone

Description

Prints a useful summary of a high-risk zone.

Usage

## S3 method for class 'highriskzone'
summary(object, ...)

Arguments

Details

A useful description of the highriskzone object is printed. This is a method for the generic function summary.

See Also

summary, print.highriskzone

Summary of a the evaluation of a high-risk zone

Description

Prints a useful summary of the evaluation of a high-risk zone.

Usage

## S3 method for class 'hrzeval'
summary(object, ...)

Arguments

Details

A useful description of the hrzeval object is printed. This is a method for the generic function summary.

See Also

summary, print.hrzeval

Thinning of the observations (for evaluating the method)

Description

The thinning is done by drawing independently from a Bernoulli distribution. This function is needed for functions eval_method, sim_clintens, sim_intens

Usage

thin(full, nxprob)

Arguments

Value

A list of observed and unobserved point patterns. Both of class ppp.

See Also

rbinom, ppp

Examples

 data(craterB)
 thdata <- thin(craterB, nxprob=0.1)
 thdata
 plot(thdata$observed); points(thdata$unobserved, col=4)