  We present a systematic study of the unbinned, photon-by-photon likelihood
technique which can be used as an alternative method to analyse
phase-dependent, X-ray spectro-polarimetric observations obtained with IXPE and
other photo-electric polarimeters. We apply the unbinned technique to models of
the luminous X-ray pulsar Hercules X-1, for which we produce simulated
observations using ixpeobssim package. We consider minimal knowledge about the
actual physical process responsible for the polarized emission from the
accreting pulsar and assume that the observed phase-dependent polarization
angle can be described by the rotating vector model. Using the unbinned
technique, the detector's modulation factor, and the polarization information
alone, we found that both the rotating vector model and the underlying
spectro-polarimetry model can reconstruct equally well the geometric
configuration angles of the accreting pulsar. However, the measured
polarization fraction becomes biased with respect to underlying model unless
the energy dispersion and effective area of the detector are also taken into
account. To this end, we present an energy-dispersed likelihood estimator that
is proved to be unbiased. For different analyses, we obtain posterior
distributions from multiple ixpeobssim realizations and show that the unbinned
technique yields $\sim 10\%$ smaller error bars than the binned technique. We
also discuss alternative sources, such as magnetars, in which the unbinned
technique and the rotating vector model might be applied.
