Redshift estimates for fast radio bursts and implications on
  intergalactic magnetic fields
  Context: Fast Radio Bursts are transient radio pulses from presumably compact
stellar sources of extragalactic origin. With new telescopes detecting multiple
events per day, statistical methods are required in order to interpret
observations and make inferences regarding astrophysical and cosmological
questions. Purpose: We present a method that uses probability estimates of fast
radio burst observables to obtain likelihood estimates for the underlying
models. Method: Considering models for all regions along the line-of-sight,
including intervening galaxies, we perform Monte-Carlo simulations to estimate
the distribution of the dispersion measure, rotation measure and temporal
broadening. Using Bayesian statistics, we compare these predictions to
observations of Fast Radio Bursts. Results: By applying Bayes theorem, we
obtain lower limits on the redshift of Fast Radio Bursts with extragalactic DM
$\gtrsim 400$ pc cm$^{-3}$. We find that intervening galaxies cannot account
for all highly scattered Fast Radio Bursts in FRBcat, thus requiring a denser
and more turbulent environment than a SGR 1935+2154-like magnetar. We show that
a sample of $\gtrsim 10^3$ unlocalized Fast Radio Bursts with associated
extragalactic RM $\geq 1$ rad m$^{-2}$ can improve current upper limits on the
strength of intergalactic magnetic fields.
