BeyondPlanck. VI. Noise characterization and modeling

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