Английская Википедия:Bhattacharyya angle
In statistics, Bhattacharyya angle, also called statistical angle, is a measure of distance between two probability measures defined on a finite probability space. It is defined as
- <math> \Delta(p,q) = \arccos \operatorname{BC}(p,q) </math>
where pi, qi are the probabilities assigned to the point i, for i = 1, ..., n, and
- <math> \operatorname{BC}(p,q) = \sum_{i=1}^n \sqrt{p_i q_i} </math>
is the Bhattacharya coefficient.[1]
The Bhattacharya distance is the geodesic distance in the orthant of the sphere <math>S^{n-1}</math> obtained by projecting the probability simplex on the sphere by the transformation <math>p_i \mapsto \sqrt{p_i},\ i=1,\ldots, n</math>.
This distance is compatible with Fisher metric. It is also related to Bures distance and fidelity between quantum states as for two diagonal states one has
- <math>\Delta(\rho,\sigma) = \arccos \sqrt{F(\rho, \sigma)}.</math>
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