Condensed Matter and Statistical Physics Journal Club
|Date:|| February 16, 2009
|| On the convex hull of random samples
|| Julien Randon-Furling (Orsay, France)
Given a random sample (eg a random set of points or a random trajectory), one can gain information about its shape via the minimum convex curve fully enclosing it, ie its convex hull.
Examples of fields where convex hulls of statistical samples are used include ecology (for home ranges of animals) and biology (for comparisons of DNA sequences).
How sensitive are quantities like the average perimeter, area and number of vertices of the convex hull to the distribution of the sample? We address this question with a general method working for both discrete and continuous samples.