Estimating information amount under uncertainty: algorithmic solvability and computational complexity

Sometimes, we know the probability of different values of the estimation error ∆x def = e x− x, sometimes, we only know the interval of possible values of ∆x, sometimes, we have interval bounds on the cdf of ∆x. To compare different measuring instruments, it is desirable to know which of them brings more information – i.e., it is desirable to gauge the amount of information. For probabilistic uncertainty, this amount of information is described by Shannon’s entropy; similar measures can be developed for interval and other types of uncertainty. In this paper, we analyze the computational complexity of the problem of estimating information amount under different types of uncertainty.