  For a track based polarimeter, such as the Imaging X-ray Polarimetry Explorer
(IXPE), the sensitivity to polarization depends on the modulation factor, which
is a strong function of energy. In previous work, a likelihood method was
developed that would account for this variation in order to estimate the
minimum detectable polarization (MDP). That method essentially required that
the position angles of individual events should be known precisely. In a
separate work, however, it was shown that using a machine learning method for
measuring event tracks can generate track angle uncertainties, which can be
used in the analysis. Here, the maximum likelihood method is used as a basis
for revising the estimate of the MDP in a general way that can include
uncertainties in event track position angles. The resultant MDP depends solely
upon the distribution of track angle uncertainties present in the input data.
Due to the physics of the IXPE detectors, it is possible to derive a simple
relationship between these angular uncertainties and the energy-dependent
modulation function as a step in the process.
