det_guard_width: Estimation of width of a guard region given an estimated...

In highriskzone: Determining and Evaluating High-Risk Zones

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

highriskzone	the estimated highriskzone for the evaluation area
thresh_const	the constant multiplied with the determined threshold, 0 < thresh_const < 1.

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)

highriskzone documentation built on Aug. 29, 2023, 3:01 p.m.