BeyondPlanck I. Global Bayesian analysis of the Planck Low Frequency
  Instrument data
  We describe the BeyondPlanck project in terms of motivation, methodology and
main products, and provide a guide to a set of companion papers that describe
each result in fuller detail. Building directly on experience from ESA's Planck
mission, we implement a complete end-to-end Bayesian analysis framework for the
Planck Low Frequency Instrument (LFI) observations. The primary product is a
joint posterior distribution P(omega|d), where omega represents the set of all
free instrumental (gain, correlated noise, bandpass etc.), astrophysical
(synchrotron, free-free, thermal dust emission etc.), and cosmological (CMB
map, power spectrum etc.) parameters. Some notable advantages of this approach
are seamless end-to-end propagation of uncertainties; accurate modeling of both
astrophysical and instrumental effects in the most natural basis for each
uncertain quantity; optimized computational costs with little or no need for
intermediate human interaction between various analysis steps; and a complete
overview of the entire analysis process within one single framework. As a
practical demonstration of this framework, we focus in particular on low-l CMB
polarization reconstruction, paying special attention to the LFI 44 GHz
channel. We find evidence of significant residual systematic effects that are
still not accounted for in the current processing, but must be addressed in
future work. These include a break-down of the 1/f correlated noise model at 30
and 44 GHz, and scan-aligned stripes in the Southern Galactic hemisphere at 44
GHz. On the Northern hemisphere, however, we find that all results are
consistent with the LCDM model, and we constrain the reionization optical depth
to tau = 0.067 +/- 0.016, with a low-resolution chi-squared
probability-to-exceed of 16%. The marginal CMB dipole amplitude is 3359.5 +/-
1.9 uK. (Abridged.)
