  A probabilistic query may not be estimable from observed data corrupted by
missing values if the data are not missing at random (MAR). It is therefore of
theoretical interest and practical importance to determine in principle whether
a probabilistic query is estimable from missing data or not when the data are
not MAR. We present an algorithm that systematically determines whether the
joint probability is estimable from observed data with missing values, assuming
that the data-generation model is represented as a Bayesian network containing
unobserved latent variables that not only encodes the dependencies among the
variables but also explicitly portrays the mechanisms responsible for the
missingness process. The result significantly advances the existing work.
