Introduction to Uncertainty with Visual, Experimental, and Computational Considerations

Marcos A. Capistrán ()
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Marcos A. Capistrán: Centro de Investigación en Matemáticas A.C. Unidad Mérida

A chapter in Handbook of Visual, Experimental and Computational Mathematics, 2026, pp 1749-1755 from Springer

Abstract: Abstract This chapter frames the scope of uncertainty quantification, mathematical modeling, and inverse problems as core tools for decision-making under imperfect models and noisy data, integrating visual, experimental, and computational perspectives. It distinguishes stochastic and epistemic uncertainty, motivates Bayesian inference for hypothesis testing and model selection, and emphasizes the ill-posed and ill-conditioned nature of inverse problems, which require joint treatment by statistics, mathematics, and computation. The chapter then presents three representative case studies: optimization-based MCMC for large-scale Poisson imaging (Bardsley, Sample-Based Uncertainty Quantification for Inverse Problems with Poisson Data. Springer Nature Switzerland, Cham, pp 1–21, 2023), Bayesian inversion for fractional-order models of cell migration with memory effects (Ariza-Hernandez et al., Bayesian Inversion in Fractional Models for Cell Migration, Springer Nature Switzerland, Cham, pp 1–21, 2023), and Bayesian, variational, and neural approaches to uncertainty quantification in epidemiological SEIR models using COVID-19 data (Palafox González et al., An Introduction to Neural Networks for Uncertainty Quantification in Epidemiological Models, Springer Nature Switzerland, Cham, pp 1–45, 2023). Together, these examples show the trade-offs between accuracy, scalability, and computational cost in modern uncertainty-aware inference.

Keywords: Uncertainty quantification; Mathematical modeling; Decision-making; Bayesian inference; Loss function; Computer models (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/978-3-032-16368-4_94

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