Noisy-OR detection by patrols

The chance that an incident is seen by patrols when each officer within radius of it sees it independently with probability p: with k officers in range, 1 - (1 - p)^k (the detection model of Barman and Barman 2026). With draw = TRUE, one detection outcome is drawn for each incident. A model of who is seen, under stated assumptions; how patrols are actually placed and how much they see are matters of fact the model does not settle.

Usage

nordet(x, off, radius, p = 0.85, draw = FALSE, seed = NULL)

Arguments

x

The incidents: a numeric matrix of two columns, or a data frame with columns x and y (or two columns), planar coordinates.

off

The officers, in the same forms; NULL or no rows for none.

radius

The range: one positive number, in the coordinates' units (distances are Euclidean; an officer exactly at radius counts).

p

The chance one officer in range sees an incident: one number above 0 and at most 1.

draw

TRUE to draw whether each incident is detected.

seed

NULL to draw the seed of the detections from R's generator, or one whole number from 0; read only with draw.

Value

A data frame with one row per incident: k (officers in range), prob and, with draw, det (1 detected, 0 not).

References

Barman, P. K. and Barman, P. K. (2026). Spatial disparities in simulated patrol detection: a reproducible generative-model audit across Baltimore and Chicago. doi:10.48550/arXiv.2603.18987

Examples

set.seed(1)
inc <- matrix(runif(20), ncol = 2)
off <- matrix(runif(10), ncol = 2)
nordet(inc, off, radius = 0.3, p = 0.7)
#>    k prob
#> 1  2 0.91
#> 2  2 0.91
#> 3  0 0.00
#> 4  2 0.91
#> 5  1 0.70
#> 6  2 0.91
#> 7  0 0.00
#> 8  0 0.00
#> 9  1 0.70
#> 10 1 0.70