  We demonstrate a new Bayesian technique to invert color-magnitude diagrams of
main sequence and white dwarf stars to reveal the underlying cluster properties
of age, distance, metallicity, and line-of-sight absorption, as well as
individual stellar masses. The advantages our technique has over traditional
analyses of color-magnitude diagrams are objectivity, precision, and explicit
dependence on prior knowledge of cluster parameters. Within the confines of a
given set of often-used models of stellar evolution, the initial-final mass
relation, and white dwarf cooling, and assuming photometric errors that one
could reasonably achieve with the Hubble Space Telescope, our technique yields
exceptional precision for even modest numbers of cluster stars. For clusters
with 50 to 400 members and one to a few dozen white dwarfs, we find typical
internal errors of sigma([Fe/H]) <= 0.03 dex, sigma(m-M) <= 0.02 mag, and
sigma(Av) <= 0.01 mag. We derive cluster white dwarf ages with internal errors
of typically only 10% for clusters with only three white dwarfs and almost
always <= 5% with ten white dwarfs. These exceptional precisions will allow us
to test white dwarf cooling models and standard stellar evolution models
through observations of white dwarfs in open and globular clusters.
