How to estimate filter coefficients of an all-pole system? Suppose we have measured the frequency response of a system that is known to be all-pole; measuring impulse response is not possible. What are the methods available, if any, to estimate the coefficients of the underlying IIR filter?

EDIT: Frequency response exists only as measured data, so closed mathematical expression is not available, nor is the phase information.
Half of the information about a system is in the phase response, and half of it in the amplitude response. There's no way to reconstruct a filter if you know only either half, unless you strongly restrict the poles mathematically.