  End-to-end simulations play a key role in the analysis of any
high-sensitivity CMB experiment, providing high-fidelity systematic error
propagation capabilities unmatched by any other means. In this paper, we
address an important issue regarding such simulations, namely how to define the
inputs in terms of sky model and instrument parameters. These may either be
taken as a constrained realization derived from the data, or as a random
realization independent from the data. We refer to these as Bayesian and
frequentist simulations, respectively. We show that the two options lead to
significantly different correlation structures, as frequentist simulations,
contrary to Bayesian simulations, effectively include cosmic variance, but
exclude realization-specific correlations from non-linear degeneracies.
Consequently, they quantify fundamentally different types of uncertainties, and
we argue that they therefore also have different and complementary scientific
uses, even if this dichotomy is not absolute. Before BeyondPlanck, most
pipelines have used a mix of constrained and random inputs, and used the same
hybrid simulations for all applications, even though the statistical
justification for this is not always evident. BeyondPlanck represents the first
end-to-end CMB simulation framework that is able to generate both types of
simulations, and these new capabilities have brought this topic to the
forefront. The Bayesian BeyondPlanck simulations and their uses are described
extensively in a suite of companion papers. In this paper we consider one
important applications of the corresponding frequentist simulations, namely
code validation. That is, we generate a set of 1-year LFI 30 GHz frequentist
simulations with known inputs, and use these to validate the core low-level
BeyondPlanck algorithms; gain estimation, correlated noise estimation, and
mapmaking.
