The notion of exchangeability referring to random events is investigated by using a geometric scheme of representation of possible alternatives. When we distribute among them our sensations of probability, we point out the multilinear essence of exchangeability by means of this scheme. Since we observe a natural one-to-one correspondence between multilinear maps and linear maps, we are able to underline that linearity concept is the most meaningful mathematical concept of probability theory. Exchangeability hypothesis is maintained for mixtures of Bernoulli processes in the same way. We are the first in the world to do this kind of work and for this reason we believe that it is inevitable that our references limit themselves only to those pioneering works which do not keep the real and deep meaning of probability concept a secret, unlike the current ones.

On a geometric extension of the notion of exchangeability referring to random events / Angelini, Pierpaolo; De Sanctis, Angela. - In: INTERNATIONAL JOURNAL OF STATISTICS AND PROBABILITY. - ISSN 1927-7032. - (2018).

On a geometric extension of the notion of exchangeability referring to random events

Angelini, Pierpaolo
;
2018

Abstract

The notion of exchangeability referring to random events is investigated by using a geometric scheme of representation of possible alternatives. When we distribute among them our sensations of probability, we point out the multilinear essence of exchangeability by means of this scheme. Since we observe a natural one-to-one correspondence between multilinear maps and linear maps, we are able to underline that linearity concept is the most meaningful mathematical concept of probability theory. Exchangeability hypothesis is maintained for mixtures of Bernoulli processes in the same way. We are the first in the world to do this kind of work and for this reason we believe that it is inevitable that our references limit themselves only to those pioneering works which do not keep the real and deep meaning of probability concept a secret, unlike the current ones.
2018
boolean algebra; boolean ring; vector space; metric; isomorphism; multilinear product
01 Pubblicazione su rivista::01a Articolo in rivista
On a geometric extension of the notion of exchangeability referring to random events / Angelini, Pierpaolo; De Sanctis, Angela. - In: INTERNATIONAL JOURNAL OF STATISTICS AND PROBABILITY. - ISSN 1927-7032. - (2018).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1266708
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