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Pré-Publication, Document De Travail Année : 2023

On Outliers

Samuel Epstein

Résumé

An outlier is an observation that is set apart from a population. There are many reasons that such anomalies occur, including measurement error and human error. This manuscript proves that outliers are ingrained into the nature of algorithms and dynamics. By modelling outliers using the discrete and continuous randomness deficiency, in this manuscript, it is proven that computable sampling methods have to produce outliers. But what about measurements of systems that are too complex to be considered algorithmic? One example is the global weather system. One can attest to the fact that there are many strange formations that occur! To show that anomalies occur, one can use the Independence Postulate. The Independence Postulate is a finitary Church-Turing thesis, postulating that certain finite and infinite sequences cannot be easily be found with a short "physical address". In this manuscript the Independence Postulate is used to show that observations, a.k.a. infinite sequences of natural numbers or reals, that do not have outliers have high physical addresses. In other words, observations with no outliers cannot be found in nature. In addition we show that outliers occur almost surely with respect to computable dynamics.
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Dates et versions

hal-04285958 , version 1 (14-11-2023)

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  • HAL Id : hal-04285958 , version 1

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Samuel Epstein. On Outliers. 2023. ⟨hal-04285958⟩
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