The “inside cell” ratio

Let \( C_s = \{c _1 , c_2 , …d_n \}\) be the
set of cells at scale \(s\) where the occurrences of a node X where found. The \(C _{s−1} = \{d_ 1 , d_ 2 , …d _k \}\) is
the corresponding set of cells at an upper scale (ancestor of \(s \)) where the occurrences of a node X where found.

Note that the ratio:
\(r_s = \frac{\#C_{s-1}}{\#C_s}\)

gives us an indicator of how the occurrences are dispersed in the space.

If \(r_s\) is low means that the
spatial distribution is constrained in a region as small as the unit area of the upper scale while if \(r_s\) is close to 1 it tells us that the occurrences are as spatially distributed as the cells in the upper scale.
The method can be applied recursively to the sucessive scales to obtain a list of ratios \(r_1 , r_2 , ..r_s ,.. \) that can be fitted in model to estimate geographic extensions.

Published by

Juan Escamilla Mólgora

I'm a mathematical and computational statistical ecologist working at the intersection of Spatial Statistics, Software Development, Machine Learning and Cloud Computing. I'm researching novel methods for integration, harmonization and modelling of big environmental data. I developed the Wild Fire Alert and Monitoring System for Mexico and Central America

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