Phys. Rev. Lett. 78, 4671–4674 (1997)Reparametrization Invariant Statistical Inference and GravityReceived 19 March 1997; published in the issue dated 23 June 1997 Bialek, Callan, and Strong have recently given a solution of the problem of determining a continuous probability distribution from a finite set of experimental measurements by formulating it as a one-dimensional quantum field theory. This Letter gives a reparametrization invariant solution of the problem, obtained by coupling to gravity. The case of a large number of dimensions is also formulated geometrically, and solved, in terms of metrics of vanishing Weyl curvature. © 1997 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.78.4671
DOI:
10.1103/PhysRevLett.78.4671
PACS:
02.50.Fz, 03.70.+k, 04.60.Kz, 11.10.Kk
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