In clinical practice one often encounters a situation when a quantity of interest cannot be measured routinely, for reasons such as invasiveness, high costs, the need for special equipment, etc. For instance, research showed that early cognitive decline can be predicted from volume (atrophy) of the nucleus basalis of Meynert (NBM), however its small size makes it difficult to measure from brain magnetic resonance (MR) scans. We treat NBM volume as an unobservable quantity in a statistical model, exploiting the structural integrity of the brain, and aim to estimate it indirectly based on one or more interdependent, but possibly more accurate and reliable compartmental brain volume measurements that are easily accessible. We propose a Bayesian approach based on the previously published reference-free error estimation framework to achieve this aim. The main contribution is a novel prior distribution parametrization encoding the scale of the distribution of the unobservable quantity. The proposed prior is more general and better interpretable than the original. In addition to unobservable quantity estimates, for each observable we calculate a figure of merit as an individual predictor of the unobservable quantity. The framework was successfully validated on synthetic data and on a clinical dataset, predicting the NBM volume from volumes of the whole-brain and hippocampal subfields, based on compartmental segmentations of structural brain MR images.