Often we are unable to directly measure quantities of interest, because of constraints on time, budget and safety. Instead we must infer these quantities from a combination of the measurements which we do have, and our understanding of the physical characteristics of the system. Sadly, neither our measurements nor our physical understanding are ever perfect, and naive combinations of the two can often lead to nonsensical, or worse, subtly wrong estimates of parameters.
One possible solution to this problem comes from Bayesian statistics, which allows for the management of uncertainty in a systematic way, while also providing mathematically rigorous ways to incorporate prior knowledge about the system.
One particular challenge in glaciology lies in estimating the topography beneath a glacier from scattered measurements of ice thickness. Recently, I developed a software package which combines a Bayesian treatment of measurement uncertainties with a physically-based flux conservation technique. This method shows great promise in reducing the amount of manual quality control required on input data.