  While considerable advance has been made to account for statistical
uncertainties in astronomical analyses, systematic instrumental uncertainties
have been generally ignored. This can be crucial to a proper interpretation of
analysis results because instrumental calibration uncertainty is a form of
systematic uncertainty. Ignoring it can underestimate error bars and introduce
bias into the fitted values of model parameters. Accounting for such
uncertainties currently requires extensive case-specific simulations if using
existing analysis packages. Here we present general statistical methods that
incorporate calibration uncertainties into spectral analysis of high-energy
data. We first present a method based on multiple imputation that can be
applied with any fitting method, but is necessarily approximate. We then
describe a more exact Bayesian approach that works in conjunction with a Markov
chain Monte Carlo based fitting. We explore methods for improving computational
efficiency, and in particular detail a method of summarizing calibration
uncertainties with a principal component analysis of samples of plausible
calibration files. This method is implemented using recently codified Chandra
effective area uncertainties for low-resolution spectral analysis and is
verified using both simulated and actual Chandra data. Our procedure for
incorporating effective area uncertainty is easily generalized to other types
of calibration uncertainties.
