  A longstanding problem in quantum metrology is how to extract as much
information as possible in realistic scenarios with not only multiple unknown
parameters, but also limited measurement data and some degree of prior
information. Here we present a practical solution to this: we derive a new
Bayesian multi-parameter quantum bound, construct the optimal measurement when
our bound can be saturated for a single shot and consider experiments involving
a repeated sequence of these measurements. Our method properly accounts for the
number of measurements and the degree of prior information, and we illustrate
our ideas with a qubit sensing network and a model for phase imaging,
clarifying the non-asymptotic role of local and global schemes. Crucially, our
technique is a powerful way of implementing quantum protocols in a wide range
of practical scenarios that tools such as the Helstrom and Holevo
Cram\'{e}r-Rao bounds cannot normally access.
