The Society for Imprecise Probabilities:
Theories and Applications

Blog category: Books

These are all the posts in the Books category of the SIPTA blog, but you can also view all blog posts.

A report on "Inferential Models", a framework for prior-free imprecise-probabilistic inference

Posted on June 6, 2021 in Books by Ryan Martin (edited by Ignacio Montes)

The book Inferential Models develops a new framework for statistical inference, one that assumes no prior, but returns (something like) a posterior probability distribution that can be used for drawing inferences. Moreover, that probability-like output satisfies a strong calibration property, called validity, which, among other things, implies that procedures derived from it provably control frequentist error rates. How is this related to imprecise probability? Indeed, this is not a book about imprecise probability, but it turns out that the inferential model’s probability-like output must be imprecise in order to achieve the validity property. Therefore, random sets, belief/plausibility functions, etc., play an important role in the development of this theory of statistical inference.

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A report on the book ''Random sets and random fuzzy sets as ill-perceived random variables''

Posted on November 11, 2014 in Books by Inés Couso

Random sets and random fuzzy sets as ill-perceived random variables. An introduction for PhD students and practitioners, by Inés Couso, Didier Dubois and Luciano Sánchez. Springer Briefs in Applied Sciences and Technology, subcategories: Springer Briefs in Computational Intelligence. 2014. The notion of random set has been around for about 50 years, and has been considered rather independently by two sets of prominent authors. There are the works published in the mid-sixties by well-known economists like Aumann and Debreu on the integration of set-valued functions, followed by a full-fledged mathematical development by Kendall and Matheron.

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Two New Books on Imprecise Probability Theories

Posted on July 17, 2014 in Books by Matthias C. M. Troffaes

Recently, two books have been published on imprecise probability theory. Lower Previsions: a monograph on said subject by myself and Gert de Cooman. Introduction to Imprecise Probabilities: a collection of contributed chapters on a wide range of topics, edited by Thomas Augustin, Frank Coolen, Gert de Cooman, and myself, with contributions from Joaquín Abellán, Alessandro Antonucci, Cassio P. de Campos, Giorgio Corani, Sébastien Destercke, Didier Dubois, Robert Hable, Filip Hermans, Nathan Huntley, Andrés Masegosa, Enrique Miranda, Serafín Moral, Michael Oberguggenberger, Erik Quaeghebeur, Glenn Shafer, Damjan Skulj, Michael Smithson, Lev Utkin, Gero Walter, Vladimir Vovk, Paolo Vicig, and Marco Zaffalon.

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