Graded set-membership models

The values of the parameters or state variables of a set-membership model are classified only as feasible (consistent with the observations and with specified bounds on output error and unknown forcing) or not. Such classification is compatible with worst-case design or prediction, but uninformative about the average quality of fit to the observations. Also, it neglects any distributional information which may be available. The paper addresses the problem of grading the feasible set, according to how well each feasible value matches the data or whether it meets simple requirements on distribution. Computing load and approximation are considered.