Confidence sub-contour box: an alternative to traditional confidence intervals

Parameter and initial conditions (factors) estimation is a challenging task in non-linear models. Even if researchers successfully estimate those model factors, they still should estimate their confidence intervals, which could require a high computational cost to turn them into informative values. Some methods in the literature attempt to estimate regions within the search space where factors may jointly exist and fit the experimental data, i.e., confidence contours. However, the estimation of such confidence contours comes up with several issues as the number of factors increases. In this work we propose a method to compute a region within the confidence contour of an inverse problem, we denote this region as the confidence sub-contour box (CSB). To estimate a CSB of an inverse problem, we propose two main algorithms alongside their interpretation and validation, testing their performance with two epidemiological models for different diseases and different kinds of data. Moreover, we exposed some desirable properties of the method through numerical experiments, such as user-defined uncertainty level, asymmetry of the resultant intervals regarding the nominal value, sensitivity assessment related to the interval length for each factor, and identification of true-influential factors. We set available all the algorithms we used in this paper at Mathworks in the GSUA-CSB toolbox.