  In this second part of our two-part paper, we provide a detailed, frequentist
framework for propagating uncertainties within our multivariate linear least
squares model. This permits us to quantify the impact of uncertainties in
thermodynamic measurements---arising from calibrations and the data acquisition
system---and the correlations therein, along with uncertainties in probe
positions. We show how the former has a much larger effect (relatively) than
uncertainties in probe placement.
  We use this non-deterministic framework to demonstrate why the well-worn
metric for assessing spatial sampling uncertainty falls short of providing an
accurate characterization of the effect of a few spatial measurements. In other
words, it does not accurately describe the uncertainty associated with sampling
a non-uniform pattern with a few circumferentially scattered rakes. To this
end, we argue that our data-centric framework can offer a more rigorous
characterization of this uncertainty. Our paper proposes two new uncertainty
metrics: one for characterizing spatial sampling uncertainty and another for
capturing the impact of measurement imprecision in individual probes. These
metrics are rigorously derived in our paper and their ease in computation
permits them to be widely adopted by the turbomachinery community for carrying
out uncertainty assessments.
