  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 unknown
parameters of this MaxEnt distribution are then handled in such a way that the
weak anthropic principle is not violated. 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 to 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.
