  We present a null-stream-based Bayesian unmodeled framework to probe generic
gravitational-wave polarizations. Generic metric theories allow six
gravitational-wave polarization states, but general relativity only permits the
existence of two of them namely the tensorial polarizations. The strain signal
measured by an interferometer is a linear combination of the polarization modes
and such a linear combination depends on the geometry of the detector and the
source location. The detector network of Advanced LIGO and Advanced Virgo
allows us to measure different linear combinations of the polarization modes
and therefore we can constrain the polarization content by analyzing how the
polarization modes are linearly combined. We propose the basis formulation to
construct a null stream along the polarization basis modes without requiring
modeling the basis explicitly. We conduct a mock data study and we show that
the framework is capable of probing pure and mixed polarizations in the
Advanced LIGO-Advanced Virgo 3-detector network without knowing the sky
location of the source from electromagnetic counterparts. We also discuss the
effect of the presence of the uncaptured orthogonal polarization component in
the framework, and we propose using the plug-in method to test the existence of
the orthogonal polarizations.
