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This question is related to Distribution of estimator of multiple (spatially related) proportions. We consider here the /visualisation/ issue.

Consider a spatial random process $Z(s)$, where $s$ denotes the spatial location.

Our objective is to delineate the zone $\mathcal{Z}$ where the probability that $Z$ exceed a given threshold $\zeta$ is above a specified probability $r$:

$$ \mathcal{Z} = \{s | \mathrm{Pr} (Z(s) > \zeta) > r\} .$$

Displaying the estimate of the zone is straighforward using two colours (“exceed” and “not exceed”), or a drawing a fontier.

Now, assume that we have access to

  • either the distribution of the estimator,
  • or confidence bounds (for each considered location $s$.

Getting one of those is the subject of another question (Distribution of estimator of multiple (spatially related) proportions).

How would you display the exceedance zone such that a non mathematician can use the map to take decision regarding where to sparingly perform an expensive action wherever the threshold is exceeded. Put another way, assume $r$ is low (1-5%) and we want to ward of the error of non acting despite threshold exceedance.

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Following my answer to the other question, you can use the local value of $\hat{P}(Z>\xi)$ and display it with a colormap, plus a contour of the zone where it exceeds $r$.

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