  Motivated by the order-of-magnitude difference in the frequency of giant
planets orbiting M dwarfs inferred by microlensing and radial velocity (RV)
surveys, we present a method for comparing the statistical constraints on
exoplanet demographics inferred from these methods. We first derive the mapping
from the observable parameters of a microlensing-detected planet to those of an
analogous planet orbiting an RV-monitored star. Using this mapping, we predict
the distribution of RV observables for the planet population inferred from
microlensing surveys, taking care to adopt reasonable priors for, and properly
marginalize over, the unknown physical parameters of microlensing-detected
systems. Finally, we use simple estimates of the detection limits for a
fiducial RV survey to predict the number and properties of analogs of the
microlensing planet population such an RV survey should detect. We find that RV
and microlensing surveys have some overlap, specifically for super-Jupiter mass
planets ($m_p \gtrsim 1~M_{\rm Jup}$) with periods between $\sim 3-10~$years.
However, the steeply falling planetary mass function inferred from microlensing
implies that, in this region of overlap, RV surveys should infer a much smaller
frequency than the overall giant planet frequency ($m_p\gtrsim 0.1~M_{\rm
Jup}$) inferred by microlensing. Our analysis demonstrates that it is possible
to statistically compare and synthesize data sets from multiple exoplanet
detection techniques in order to infer exoplanet demographics over wider
regions of parameter space than are accessible to individual methods. In a
companion paper, we apply our methodology to several representative
microlensing and RV surveys to derive the frequency of planets around M dwarfs
with orbits of $\lesssim 30~$years.
