  The Ramsey sequence is a canonical example of a quantum phase measurement for
a spin qubit. In Ramsey measurements, the measurement efficiency can be
optimized through careful selection of settings for the phase accumulation time
setting, $\tau$. This paper implements a sequential Bayesian experiment design
protocol for the phase accumulation time in low-fidelity Ramsey measurements,
and performance is compared to both a previously reported adaptive heuristic
protocol and random setting choices. A workflow allowing measurements and
design calculations to run concurrently largely eliminates computation time
from measurement overhead. When precession frequency is the lone parameter to
estimate, the Bayesian design is faster by factors of 2 and 4 relative to the
adaptive heuristic and random protocols respectively.
