Information about the physical properties of astrophysical objects cannot be
measured directly but is inferred by interpreting spectroscopic observations in
the context of atomic physics calculations. Ratios of emission lines, for
example, can be used to infer the electron density of the emitting plasma.
Similarly, the relative intensities of emission lines formed over a wide range
of temperatures yield information on the temperature structure. A critical
component of this analysis is understanding how uncertainties in the underlying
atomic physics propagates to the uncertainties in the inferred plasma
parameters. At present, however, atomic physics databases do not include
uncertainties on the atomic parameters and there is no established methodology
for using them even if they did. In this paper we develop simple models for the
uncertainties in the collision strengths and decay rates for Fe XIII and apply
them to the interpretation of density sensitive lines observed with the EUV
Imagining spectrometer (EIS) on Hinode. We incorporate these uncertainties in a
Bayesian framework. We consider both a pragmatic Bayesian method where the
atomic physics information is unaffected by the observed data, and a fully
Bayesian method where the data can be used to probe the physics. The former
generally increases the uncertainty in the inferred density by about a factor
of 5 compared with models that incorporate only statistical uncertainties. The
latter reduces the uncertainties on the inferred densities, but identifies
areas of possible systematic problems with either the atomic physics or the
observed intensities.Comment: in press at Ap
