Set inversion via interval analysis for nonlinear bounded-error estimation
Automatica (Journal of IFAC) - Special section on fault detection, supervision and safety for technical processes
ILPS '94 Proceedings of the 1994 International Symposium on Logic programming
Revising hull and box consistency
Proceedings of the 1999 international conference on Logic programming
Uncertainty in Constraint Satisfaction Problems: a Probalistic Approach
ECSQARU '93 Proceedings of the European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty
Universally Quantified Interval Constraints
CP '02 Proceedings of the 6th International Conference on Principles and Practice of Constraint Programming
Reasoning about Uncertainty
Parameter Estimation Using Interval Computations
SIAM Journal on Scientific Computing
Inverse Problem Theory and Methods for Model Parameter Estimation
Inverse Problem Theory and Methods for Model Parameter Estimation
Algorithm 852: RealPaver: an interval solver using constraint satisfaction techniques
ACM Transactions on Mathematical Software (TOMS)
An adaptive Monte Carlo integration algorithm with general division approach
Mathematics and Computers in Simulation
Probabilistic Continuous Constraint Satisfaction Problems
ICTAI '08 Proceedings of the 2008 20th IEEE International Conference on Tools with Artificial Intelligence - Volume 02
Consistency techniques for numeric CSPs
IJCAI'93 Proceedings of the 13th international joint conference on Artifical intelligence - Volume 1
Constraint solving over semirings
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
A constraint satisfaction framework for decision under uncertainty
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
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The probabilistic continuous constraint framework complements the representation of uncertainty by means of intervals with a probabilistic distribution of values within such intervals. This paper describes how nonlinear inverse problems can be cast into this framework, highlighting its ability to deal with all the uncertainty aspects of such problems. In previous work we have formalized the framework, relying on simplified integration methods to characterize the uncertainty distributions. In this paper we (1) provide validated constraint-based algorithms to compute these distributions, (2) discuss approximations obtained by their hybridization with Monte-Carlo methods, and (3) obtain a better uncertainty characterization, by including methods to compute expected values and standard deviations. The paper illustrates this new methodology in Ocean Color (OC), a research area which is widely used in climate change studies and has potential applications in water quality monitoring. OC semi-analytical approaches rely on forward models that relate optically active seawater compounds (OC products) to remote sensing measurements of the sea-surface reflectance. OC products are derived by inverting the forward model on a spectral-reflectance basis. Based on a set of preliminary experiments we show that the probabilistic constraint framework is able to provide a valuable characterization of the uncertainty of all scenarios consistent with the model and the measurements. Moreover, the framework can be used to derive how measurements accuracy affects the uncertainty distribution of the retrieved OC products, which may constitute an important contribution to the OC community.