Exchangeability and randomness for infinite and finite sequences

Vladimir Vovk

Exchangeability and randomness for infinite and finite sequences

Vladimir Vovk

Research output: Contribution to journal › Article › peer-review

Abstract

Randomness (in the sense of being generated in an IID fashion) and exchangeability are standard assumptions in nonparametric statistics and machine learning, and relations between them have been a popular topic of research. This short paper draws the reader’s attention to the fact that, while for infinite sequences of observations the two assumptions are almost indistinguishable, the difference between them becomes very significant for finite sequences of a given length.

Original language	English
Number of pages	10
Journal	Statistical Science
Publication status	Accepted/In press - 6 Aug 2026

Keywords

assumption of exchangeability
assumption of randomness

Access to Document

https://arxiv.org/abs/2512.22162

Embargoed Document

Accepted Manuscript
Accepted author manuscript, 600 KB
Licence: CC BY

Cite this

@article{d35d2b575b904357a1440fa89b93842f,

title = "Exchangeability and randomness for infinite and finite sequences",

abstract = "Randomness (in the sense of being generated in an IID fashion) and exchangeability are standard assumptions in nonparametric statistics and machine learning, and relations between them have been a popular topic of research. This short paper draws the reader{\textquoteright}s attention to the fact that, while for infinite sequences of observations the two assumptions are almost indistinguishable, the difference between them becomes very significant for finite sequences of a given length.",

keywords = "assumption of exchangeability, assumption of randomness",

author = "Vladimir Vovk",

year = "2026",

month = aug,

day = "6",

language = "English",

journal = "Statistical Science",

issn = "0883-4237",

publisher = "Institute of Mathematical Statistics",

}

TY - JOUR

T1 - Exchangeability and randomness for infinite and finite sequences

AU - Vovk, Vladimir

PY - 2026/8/6

Y1 - 2026/8/6

N2 - Randomness (in the sense of being generated in an IID fashion) and exchangeability are standard assumptions in nonparametric statistics and machine learning, and relations between them have been a popular topic of research. This short paper draws the reader’s attention to the fact that, while for infinite sequences of observations the two assumptions are almost indistinguishable, the difference between them becomes very significant for finite sequences of a given length.

AB - Randomness (in the sense of being generated in an IID fashion) and exchangeability are standard assumptions in nonparametric statistics and machine learning, and relations between them have been a popular topic of research. This short paper draws the reader’s attention to the fact that, while for infinite sequences of observations the two assumptions are almost indistinguishable, the difference between them becomes very significant for finite sequences of a given length.

KW - assumption of exchangeability

KW - assumption of randomness

M3 - Article

SN - 0883-4237

JO - Statistical Science

JF - Statistical Science

ER -