Model Construction of the Basic Theories of Probability Theory in the Quantification of Uncertainty

DOI: https://doi.org/10.62517/jbdc.202501425

Author(s)

Zirui Wang

Affiliation(s)

Shanghai Experimental Foreign Language School, Shanghai, China *Corresponding Author

Abstract

Probability theory, as a core mathematical tool for quantifying uncertainty, provides a scientific basis for decision-making by constructing probability models. This paper systematically reviews the model construction path of the basic theories of probability theory in the quantification of uncertainty. Starting from the theoretical framework of probability space and random variables, it analyzes the influence of parameter estimation methods on model uncertainty, explores the advantages of Bayesian inference in the quantification of cognitive uncertainty, and further elaborates on the application of probability models in the propagation of uncertainty in complex systems. Research shows that the fundamental theories of probability theory provide a full-chain methodology from data generation to decision support for the quantification of uncertainty, which is of great value in enhancing the reliability of models and the scientific nature of decisions.

Keywords

Probability Theory; Quantification of Uncertainty; Model Construction; Parameter Estimation; Bayesian Inference

References

[1] McDonald, S., & Campbell, D. (2021). A review of uncertainty quantification for density estimation. [2] Kendall, A., & Gal, Y. (2017). What uncertainties do we need in bayesian deep learning for computer vision?. Advances in neural information processing systems, 30. [3] Ross, S. M. (2020). Introduction to probability and statistics for engineers and scientists. Academic press. [4] Gal, Y., & Ghahramani, Z. (2016, June). Dropout as a bayesian approximation: Representing model uncertainty in deep learning. In international conference on machine learning (pp. 1050-1059). PMLR. [5] Pearl, J., & Mackenzie, D. (2018). The book of why: the new science of cause and effect. Basic books. [6] Durrett, R. (2019). Probability: theory and examples (Vol. 49). Cambridge University Press. [7] Ross, S. M. (2020). A first course in probability. Harlow, UK: Pearson. [8] Taleb, N. N. (2020). Statistical consequences of fat tails: Real world preasymptotics, epistemology, and applications. arXiv preprint arXiv:2001.10488.