Remote sensors in the infrared region can be used to study the progression of fireballs generated from experiments involving high explosives (HE). Developing an improved understanding of HE fireballs can be used to validate and improve computational physics codes that simulate such events. In this paper, Bayesian approaches are studied to estimate time-dependent optimal fireball parameters and their uncertainties using Fourier transform infrared (FTIR) spectroscopy. The optical signal measured by an FTIR sensor provides information on the fireball due to thermal emission, particulate emission/absorption, and HE gas product emission/absorption from the fireball. FTIR sensors have the advantage of being able to capture and measure the radiance in a large part of the infrared spectrum. The parameters to be estimated from the fireball include temperature and size, soot quantity, gas species concentrations (e.g., H2O, CO2, CO), and information on the presence of metals. In general, this inverse optimization problem is difficult due to the estimated quantities being correlated, the low spectral resolution of the FTIR sensor, and the intervening atmosphere absorbing the radiation emitted from the fireball. Bayesian calibration and Bayesian model averaging are applied to address these difficulties and to quantify the uncertainty in the estimated optimal parameter values. The fireball parameter settings are evaluated by the fit of a simplified spectral model to FTIR data. The overall problem will be presented together with a description of the Bayesian approaches. In this paper, the Bayesian approaches are applied to artificially generated FTIR data to illustrate the approach.