  A distributed binary hypothesis testing problem is studied with one observer
and two decision centers. Achievable type-II error exponents are derived for
testing against conditional independence when the observer communicates with
the two decision centers over one common and two individual noise-free bit
pipes and when it communicates with them over a noisy broadcast channel (BC).
The results are based on a coding and testing scheme that splits the
observations into subblocks, so that transmitter and receivers can
independently apply to each subblock either Gray-Wyner coordination coding with
side-information or hybrid joint source-channel coding with side-information,
followed by a Neyman-Pearson test over the subblocks at the receivers. This
approach allows to avoid introducing further error exponents that one would
expect from the receivers' decoding operations related to binning or the noisy
transmission channel. The derived exponents are shown to be optimal in some
special cases when communication is over noise-free links. The results reveal a
tradeoff between the type-II error exponents at the two decision centers.
