How to measure a degree of mismatch between probability models, p-boxes, etc.: A decision-theory-motivated utility-based approach

Different models can be used to describe real-life phenomena: deterministic, probabilistic, fuzzy, models in which we have interval-valued or fuzzy-valued probabilities, etc. Models are usually not absolutely accurate. It is therefore important to know how accurate is a given model. In other words, it is important to be able to measure a mismatch between the model and the empirical data. In this paper, we describe an approach of measuring this mismatch which is based on the notion of utility, the central notion of utility theory. We also show that a similar approach can be used to measure the loss of privacy.