  The fine-tuning of the universe for life, the idea that the constants of
nature (or ratios between them) must belong to very small intervals in order
for life to exist, has been debated by scientists for several decades. Several
criticisms have emerged concerning probabilistic measurement of life-permitting
intervals. Herein, a Bayesian statistical approach is used to assign an upper
bound for the probability of tuning, which is invariant with respect to change
of physical units, and under certain assumptions it is small whenever the
life-permitting interval is small on a relative scale. The computation of the
upper bound of the tuning probability is achieved by first assuming that the
prior is chosen by the principle of maximum entropy (MaxEnt). The MaxEnt
assumption is ``maximally noncommittal with regard to missing information.''
This approach is sufficiently general to be applied to constants of current
cosmological models, or for other constants possibly under different models.
Application of the MaxEnt model reveals, for example, that the ratio of the
universal gravitational constant to the square of the Hubble constant is finely
tuned in some cases, whereas the amplitude of primordial fluctuations is not.
