Imprecise probability books

Below are some of the imprecise probability books that material for this course will be taken from. None of these are strictly required as textbooks for the course, and none will be covered in their entirety, but it’d help if students can get access to one or more reference so they have something besides the instructor’s notes to read. NC State students can access some of the newer books electronically through the university library; students at other universities can probably get similar access through their libraries.

  • Aslett et al.’s Uncertainty in Engineering, 2022 (open access)
  • Augustin et al.’s Introduction to Imprecise Probabilities, 2014
  • Cuzzolin’s The Geometry of Uncertainty, 2021
  • Dubois & Prade’s Possibility Theory, 1988
  • Kohlas & Monney’s A Mathematical Theory of Hints, 1995
  • Molchanov’s Theory of Random Sets, 2005
  • Nguyen’s An Introduction to Random Sets, 2006
  • Shafer’s A Mathematical Theory of Evidence, 1976
  • Troffaes & De Cooman’s Lower Previsions, 2014
  • Walley’s Statistical Reasoning with Imprecise Probabilities, 1991

Related texts

Below are some books that aren’t specifically about imprecise probability, but are related in one way or another. Some material might be taken from these resources as time and energy allows. Other relevant references might be added to this list as the course progresses.

  • Huber & Ronchetti’s Robust Statistics, 2009
  • Manski’s Partial Identification of Probability Distributions, 2003
  • Martin & Liu’s Inferential Models, 2015
  • Shackle’s Decision, Order, and Time, 1961
  • Shafer & Vovk’s Game-Theoretic Foundations for Probability and Finance, 2019

Blog post on the SIPTA website

Some background on my work in this area and how I ended up connecting with and getting inspired by the imprecise probability community can be found in this blog post.

SIPTA 2020/2021 (online) school

This event was hosted by the Institute for Risk and Uncertainty at the University of Liverpool during Winter 2021. Videos of the short course lectures (including those by your instructor) are available here.

Imprecise probability professional society pages

Society of Imprecise Probability Theory & Applications

Belief Functions & Applications Society