Description Usage Arguments Details Value References See Also Examples

View source: R/bootcorrect_restr.R

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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 |

`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 |

`obsprobimage` |
(optional) an object of class |

`intens` |
(optional) estimated intensity of the observed process (object of class "im",
see |

`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 |

`radiusClust` |
(optional) radius of the circles around the parent points in which the cluster
points are located. Only used for |

`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 |

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

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.

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.

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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 | ```
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)
``` |

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