We propose a new, more general definition of extended probability measures. We study their properties and provide a behavioral interpretation. We put them to use in an inference procedure, whose environment is canonically represented by the probability space (Ω, ℱ, P), when both P and the composition of Ω are unknown. We develop an ex ante analysis — taking place before the statistical analysis requiring knowledge of Ω — in which the true composition of Ω is progressively learned. We describe how to update extended probabilities in this setting and introduce the concept of lower extended probabilities. We apply our findings to a species sampling problem and to the study of the boomerang effect (the empirical observation that sometimes persuasion yields the opposite effect: the persuaded agent moves their opinion away from the opinion of the persuading agent).
%0 Book Section
%1 caprio2025extended
%A Caprio, Michele
%A Mukherjee, Sayan
%D 2025
%K nopdf topic_mathfoundation
%P 299-352
%R 10.1142/9789811294921_0011
%T Extended probabilities and their application to statistical inference
%U https://www.worldscientific.com/doi/abs/10.1142/9789811294921_0011
%X We propose a new, more general definition of extended probability measures. We study their properties and provide a behavioral interpretation. We put them to use in an inference procedure, whose environment is canonically represented by the probability space (Ω, ℱ, P), when both P and the composition of Ω are unknown. We develop an ex ante analysis — taking place before the statistical analysis requiring knowledge of Ω — in which the true composition of Ω is progressively learned. We describe how to update extended probabilities in this setting and introduce the concept of lower extended probabilities. We apply our findings to a species sampling problem and to the study of the boomerang effect (the empirical observation that sometimes persuasion yields the opposite effect: the persuaded agent moves their opinion away from the opinion of the persuading agent).
%7 Understanding Information and Its Role as a Tool
%& 11
@inbook{caprio2025extended,
abstract = {We propose a new, more general definition of extended probability measures. We study their properties and provide a behavioral interpretation. We put them to use in an inference procedure, whose environment is canonically represented by the probability space (Ω, ℱ, P), when both P and the composition of Ω are unknown. We develop an ex ante analysis — taking place before the statistical analysis requiring knowledge of Ω — in which the true composition of Ω is progressively learned. We describe how to update extended probabilities in this setting and introduce the concept of lower extended probabilities. We apply our findings to a species sampling problem and to the study of the boomerang effect (the empirical observation that sometimes persuasion yields the opposite effect: the persuaded agent moves their opinion away from the opinion of the persuading agent).},
added-at = {2024-10-02T10:38:17.000+0200},
archiveprefix = {arXiv},
author = {Caprio, Michele and Mukherjee, Sayan},
biburl = {https://puma.scadsai.uni-leipzig.de/bibtex/2c6804e1db904a73e46fa318a313ba223/scadsfct},
chapter = 11,
doi = {10.1142/9789811294921_0011},
edition = {Understanding Information and Its Role as a Tool},
eprint = {2111.01050},
interhash = {a5ad68c349251844bdbcb44ea4b9bc57},
intrahash = {c6804e1db904a73e46fa318a313ba223},
keywords = {nopdf topic_mathfoundation},
pages = {299-352},
primaryclass = {math.ST},
timestamp = {2025-06-20T11:03:27.000+0200},
title = {Extended probabilities and their application to statistical inference},
url = {https://www.worldscientific.com/doi/abs/10.1142/9789811294921_0011},
year = 2025
}
