Documentation

This documentation page provides (pointers to) introductory reading material on imprecise probabilities (IP). It covers four books on imprecise probabilities, and provides an extensive list of tutorials and lectures on various subtopics. This documentation page has been completely redesigned in 2021. Some of the material that was available in previous versions is still available in the SIPTA archive.

Books on imprecise probabilities

From a historical point of view, there are three important reference works:

Statistical Reasoning with Imprecise Probabilities, by Peter Walley.
Elementare Grundbegriffe einer allgemeineren Wahrscheinlichkeitsrechnung I, by Kurt Weichselberger.
Interval Statistical Models, by Vladimir Kuznetsov.

Each of these books is still relevant today. The first is out of print though, and the other two are only available in German and Russian, respectively. For Kuznetsov’s book, SIPTA makes available a free copy; we are also involved in a collaborative translation of that book.

In 2014, to address the need for an easily accessible overview of the field, members of the SIPTA society wrote and edited Introduction to Imprecise Probabilities. It provides a comprehensive introduction to imprecise probabilities, covering theory as well as applications. If you’d like to know how this book came to be, you can read all about it in the following blog post.

There are also various books available that focus on specific topics within imprecise probabilities, or on specific types of models such as lower previsions, belief functions, etcetera. Searching for your topic of interest on google should get you a long way.

ISIPTA tutorials

Several ISIPTA conferences featured tutorials that provide a gentle introduction to a wide range of important topics in imprecise probability. A complete list, with links to the material, is given below.

ISIPTA 2015

Philosophical foundations of imprecise probability

G. Wheeler

ISIPTA 2011

Imprecise probability in engineering – a case study

M. Oberguggenberger

ISIPTA 2009

Graphical models

C. de Campos

Decision theory under imprecise probabilities

R. Hable

Desirability

E. Quaeghebeur

Imprecise reliability

L. Utkin

ISIPTA 2007

Risk analysis

S. Ferson

Generalized information theory

G. Klir

An introduction to the theory of coherent lower previsions

E. Miranda

ISIPTA 2005

Decision theories for imprecise preferences and imprecise probabilities

T. Seidenfeld

ISIPTA 2003

Imprecise Dirichlet model for multinomial data

J.M. Bernard

Graph-theoretical models for multivariate modeling with imprecise probabilities

F. Cozman

A gentle introduction to imprecise probability models and their behavioral interpretation

G. de Cooman

Partial identification of probability distributions

C.F. Manski

Imprecise probabilities and ambiguity aversion in economic modeling

S. Mukerji

SIPTA School lectures

Every two years, at the SIPTA School, experts on imprecise probabilities give introductory lectures about important topics in the field, both theoretical and applied. For each such topic, we here provide a selection of direct links to the material. We omit older lectures because they often have significant overlap with more recent ones; that material is still available on the websites of past schools though.

Introduction to imprecise probabilities

Introduction to imprecise probabilities

Presented by E. Quaeghebeur at the SIPTA School in 2024

[ slides ] [ video ]

Foundations of imprecise probabilities

Presented by G. de Cooman at the SIPTA School in 2022

[ slides 1 ] [ slides 2 ] [ slides 3 ] [ slides 4 ] [ video 1 ] [ video 2 ] [ video 3 ] [ video 4 ]

Introduction to imprecise probabilities

Presented by I. Montes at the SIPTA School in 2020

[ slides ] [ video 1 ] [ video 2 ] [ exercises ] [ solutions ]

The schools of 2018, 2016, 2014, 2012, 2010, 2008, 2006 and 2004 also covered this topic.

Structural judgements

Independence in imprecise probability

Presented by F. Cozman at the SIPTA School in 2012