“Bhattacharyya angle”的意思、由来-开放百科全书

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Bhattacharyya angle

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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

where p_i, q_i are the probabilities assigned to the point i, for i = 1, ..., n, and

is the Bhattacharya coefficient.^[1]

The Bhattacharya distance is the geodesic distance in the orthant of the sphere obtained by projecting the probability simplex on the sphere by the transformation .

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

References

1. ^{{Cite journal|url = |title = On a measure of divergence between two statistical populations defined by their probability distributions|last = Bhattacharya|first = Anil Kumar|date = 1943|journal = Bulletin of the Calcutta Mathematical Society|doi = |pmid = |access-date = |volume = 35|pages = 99–109}}

1 : Statistical distance

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