Accounting for Uncertainty in Instrumental Calibration
(and in Physical Constants)

Estimating parameters that quantify the physical environments of solar and stellar atmospheres requires a detailed understanding of complex instrumentation and/or atomic physics. The analysis of high-energy spectra and images in astronomy, for example, relies on prelaunch and space-based calibration of the operating characteristics of the photon detectors used for space-based data collection.(e.g., point spread functions, effective areas, etc.). Estimating the physical parameters of the solar coronae from its measured spectral emission lines, on the other hand, relies on detailed atomic physics calculations to obtain necessary underlying physical constants (e.g., emissivity functions). In both cases, statistical analyses rely on quantities that are only known approximately, and that exhibits complex correlation structures among their components. Nonetheless these quantities are typically taken as known in the final analysis.

In this talk we explore the effect of such uncertainly on parameter estimates and error bars. We then develop a suite of statistical methods that aim to properly account for this uncertainty. Our framework allows us to estimate the physical parameters of interest, the instrumental calibration functions, and/or the underlying physical constants. In principle, multiple data sets sharing common calibration functions can be combined for more precise inference. Unfortunately, however, this may allow biases stemming from misspecification in some of the analyses to spread to others. We consider how comparing the individual analyses can diagnose such bias and how the results of the combined secondary analyses can be fed back to improve estimation.

David van Dyk