eval_method: 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
)

Value

A data.frame with variables

Iteration: Iterationstep of the result
Type, Criterion, Cutoff, nxprob: see arguments
threshold: determined threshold. If criterion="area", it is either the distance (if type="dist") or the threshold c (for type="intens"). If criterion="indirect", it is either the quantile of the nearest-neighbour distance which is used as radius (if type="dist") or the threshold c (for type="intens"). If criterion="direct", it equals the cutoff for both types.
calccutoff: determined cutoff-value. For type="dist" and criterion="area", this is the quantile of the nearest-neighbour distance. For type="intens" and criterion="area", it is the failure probability alpha. For all other criterions it is NA.
covmatrix11, covmatrix12, covmatrix21, covmatrix22: values in the covariance matrix. covmatrix11 and covmatrix22 are the diagonal elements (variances).
numbermiss: number of unobserved points outside the high-risk zone
numberunobserved: number of observations in the unobserved point pattern Z'
missingfrac: fraction of unobserved events outside the high-risk zone (numbermiss/numberunobserved)
arearegion: area of the high-risk zone
numberobs: number of observations in the observed point pattern Y'

Arguments

ppdata: Observed spatial point process of class ppp.
type: Method to use, can be one of "dist" (method of fixed radius or quantile-based method), or "intens" (intensity-based method)
criterion: criterion to limit the high-risk zone, can be one of "area" (giving size of hrz), "indirect" (giving quantile/alpha depending on type), or "direct" (giving radius/threshold c depending on type)
cutoff: Value of criterion (area, radius, quantile, alpha or threshold). Depending on criterion and type: If criterion = "direct" and type = "intens", cutoff is the maximum intensity of unexploded bombs outside the risk zone. If type = "dist" instead, cutoff is the radius of the circle around each exploded bomb. "If criterion = "indirect", cutoff is the quantile for the quantile-based method and the failure probability alpha for the intensity-base method. If criterion = "area", cutoff is the area the high-risk zone should have.
numit: Number of iterations
nxprob: Probability of having unobserved events. Default value is 0.1.
distancemap: (optional) distance map: distance of every pixel to the nearest observation of the point pattern; only needed for type="dist". If not given, it will be computed by distmap.
intens: (optional) estimated intensity of the observed process (object of class "im"), only needed for type="intens". If not given, it will be estimated using density.ppp.
covmatrix: (optional) Covariance matrix of the kernel of a normal distribution, only needed for type="intens" if no intensity is given. If not given, it will be estimated using Hscv.
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 is also the parameter of the Poisson distribution for the number of points per cluster. Only used for simulate = "clintens".
pbar: logical. Should progress bar be printed?

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.

Examples

Run this code

if (FALSE) {    
 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) ))
}