  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 may involve quantum gravity restricted to metrics of vanishing Weyl
curvature.
