Bayesian Approach to Find a Long-Term Trend in Erratic Polarization
  Variations Observed in Blazars
  We developed a method to separate a long-term trend from observed temporal
variations of polarization in blazars using a Bayesian approach. The temporal
variation of the polarization vector is apparently erratic in most blazars,
while several objects occasionally exhibited systematic variations, for
example, an increase of the polarization degree associated with a flare of the
total flux. We assume that the observed polarization vector is a superposition
of distinct two components, a long-term trend and a short-term variation
component responsible for short flares. Our Bayesian model estimates the
long-term trend which satisfies the condition that the total flux correlates
with the polarized flux of the short-term component. We demonstrate that
assumed long-term polarization components are successfully separated by the
Bayesian model for artificial data. We applied this method to photopolarimetric
data of OJ 287, S5 0716+714, and S2 0109+224. Simple and systematic long-term
trends were obtained in OJ 287 and S2 0109+224, while no such a trend was
identified in S5 0716+714. We propose that the apparently erratic variations of
polarization in OJ 287 and S2 0109+224 are due to the presence of the long-term
polarization component. The behavior of polarization in S5 0716+714 during our
observation period implies the presence of a number of polarization components
having a quite short time-scale of variations.
