BeyondPlanck VI. Noise characterization and modelling
  We present a Bayesian method for estimating instrumental noise parameters and
propagating noise uncertainties within the global BeyondPlanck Gibbs sampling
framework, and apply this to Planck LFI time-ordered data. Following previous
literature, we adopt a simple $1/f$ model for the noise power spectral density
(PSD), and implement an optimal Wiener-filter (or constrained realization)
gap-filling procedure to account for masked data. We then use this procedure to
both estimate the gapless correlated noise in the time-domain,
$n_\mathrm{corr}$, and to sample the noise PSD spectral parameters, $\xi^n =
\{\sigma_0, f_\mathrm{knee}, \alpha\}$. In contrast to previous Planck
analyses, we only assume piecewise stationary noise within each pointing period
(PID), not throughout the full mission, but we adopt the LFI DPC results as
priors on $\alpha$ and $f_\mathrm{knee}$. On average, we find best-fit
correlated noise parameters that are mostly consistent with previous results,
with a few notable exceptions. However, a detailed inspection of the
time-dependent results reveals many important findings. First and foremost, we
find strong evidence for statistically significant temporal variations in all
noise PSD parameters, many of which are directly correlated with satellite
housekeeping data. Second, while the simple $1/f$ model appears to be an
excellent fit for the LFI 70 GHz channel, there is evidence for additional
correlated noise not described by a $1/f$ model in the 30 and 44 GHz channels,
including within the primary science frequency range of 0.1-1 Hz. In general,
most 30 and 44 GHz channels exhibit excess noise at the 2-$3 \sigma$ level in
each one hour pointing period. For some periods of time, we also find evidence
of strong common mode noise fluctuations across the entire focal plane.
(Abridged.)
