Posted on June 6, 2021
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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.
Posted on November 11, 2014
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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. Completely apart from this trend is the pioneering work of Dempster who studied upper and lower probabilities induced by a multivalued mapping from a probability space to the range of an attribute of interest. On this basis, Shafer theory of evidence was built. Formally this is an avatar of random set theory.
Posted on July 17, 2014
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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.
