A differential inclusion approach for modeling and analysis of dynamical systems under uncertainty

Barrios, Jorge; Pietrus, Alain; Joya, Gonzalo; Marrero, Aymée; Arazoza, Hector De

doi:10.1007/s00500-012-0889-2

Cited by 5 publications

(1 citation statement)

References 14 publications

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“…The development of mathematical models that describe real-life situations plays an important role in basic and applied research of disciplines as physics, biology, chemistry, engineering, and epidemiology [3] [4]. Those models usually depend on several factors (parameters and initial conditions) whose values are unknown or only known imprecisely [21].…”

Section: Introductionmentioning

confidence: 99%

A novel algorithm for confidence sub-contour box estimation: an alternative to traditional confidence intervals

Rojas-Díaz¹,

Catano-López²,

Velez-Sanchez³

2019

Preprint

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The factor estimation process is a really challenging task for non-linear models. Even whether researchers manage to successfully estimate model factors, they still must estimate their confidence intervals, which could require a high computational cost to turn them into informative measures. Some methods in the literature attempt to estimate regions within the estimation search space where factors may jointly exist and fit the real data (confidence contours), however, its estimation process raises several issues as the number of factors increases. Hence, in this paper, we focus on the estimation of a subregion within the confidence contour that we called as Confidence Sub-contour Box (CSB). We proposed two main algorithms for CSB estimation, as well as its interpretation and validation. Given the way we estimated CSB, we expected and validated some useful properties of this new kind of confidence interval: a user-defined uncertainty level, asymmetrical intervals, sensitivity assessment related to the interval length for each factor, and the identification of true-influential factors.

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Section: Introductionmentioning

confidence: 99%