Using Bayesian Analysis to Quantify Uncertainty in Radiometer Measurements

Abstract

We apply Bayesian inference to instrument calibration and experimental-data uncertainty analysis for the specific application of measuring radiative intensity with a narrow-angle radiometer. We develop a physics-based instrument model that describes temporally varying radiative intensity, the indirectly measured quantity of interest, as a function of scenario and model parameters. We identify a set of five uncertain parameters, find their probability distributions (the posterior or inverse problem) given the calibration data by applying Bayes’ Theorem, and employ a local linearization to marginalize the nuisance parameters resulting from errors-in-variables. We then apply the instrument model to a new scenario that is the intended use of the instrument, a 1.5 MW coal-fired furnace. Unlike standard error propagation, this Bayesian method infers values for the five uncertain parameters by sampling from the posterior distribution and then computing the intensity with quantifiable uncertainty at the point of a new, in situ furnace measurement (the posterior predictive or forward problem). Given the instrument-model context of this analysis, the propagated uncertainty provides a significant proportion of the measurement error for each in situ furnace measurement. With this approach, we produce uncertainties at each temporal measurement of the radiative intensity in the furnace, successfully identifying temporal variations that were otherwise indistinguishable from measurement uncertainty.