The Praise of Ignorance: Randomnessas Lack of Certainty. Calvetti, D. & Somersalo, E. Applied Mathematical Sciences (Switzerland), 215:81 – 93, 2023. Publisher: Springer Type: Book chapter![The Praise of Ignorance: Randomnessas Lack of Certainty [link]](https://bibbase.org/img/filetypes/link.svg "link")
Paper doi abstract bibtex After the lengthy technical introduction of the previous chapters, we are now ready to start estimating unknown quantities based on incomplete information and indirect observations. We adopt here the Bayesian point of view: Any quantity that is not known exactly, in the sense that a value can be attached to it with no uncertainty, is modeled as a random variable. In this sense, randomness means lack of certainty. The subjective part of this approach is clear: even if we believed that an underlying parameter corresponds to an existing physical quantity that could, in principle, be determined and therefore is conceptually deterministic, the lack of the subject’s information about it justifies modeling it as a random variable. The question of whether a parameter will be modeled as a random variable is then answered according to how much we know about the quantity or how strong our beliefs are. This general guiding principle will be followed throughout the rest of the book, applied to various degrees of rigor. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.
@article{calvetti_praise_2023,
title = {The {Praise} of {Ignorance}: {Randomnessas} {Lack} of {Certainty}},
volume = {215},
issn = {00665452},
url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85149947996&doi=10.1007%2f978-3-031-23824-6_5&partnerID=40&md5=c0f929c514df14d2cac71d45bda439fe},
doi = {10.1007/978-3-031-23824-6_5},
abstract = {After the lengthy technical introduction of the previous chapters, we are now ready to start estimating unknown quantities based on incomplete information and indirect observations. We adopt here the Bayesian point of view: Any quantity that is not known exactly, in the sense that a value can be attached to it with no uncertainty, is modeled as a random variable. In this sense, randomness means lack of certainty. The subjective part of this approach is clear: even if we believed that an underlying parameter corresponds to an existing physical quantity that could, in principle, be determined and therefore is conceptually deterministic, the lack of the subject’s information about it justifies modeling it as a random variable. The question of whether a parameter will be modeled as a random variable is then answered according to how much we know about the quantity or how strong our beliefs are. This general guiding principle will be followed throughout the rest of the book, applied to various degrees of rigor. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.},
language = {English},
journal = {Applied Mathematical Sciences (Switzerland)},
author = {Calvetti, Daniela and Somersalo, Erkki},
year = {2023},
note = {Publisher: Springer
Type: Book chapter},
pages = {81 -- 93},
}
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