# 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**

**ISIPTA 2011**

Imprecise probability in engineering – a case study

M. Oberguggenberger

**ISIPTA 2009**

**ISIPTA 2007**

S. Ferson

Generalized information theory

G. Klir

An introduction to the theory of coherent lower previsions

E. Miranda

**ISIPTA 2005**

**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**

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 ]

Introduction to imprecise probabilities

Presented by I. Couso & E. Miranda at the SIPTA School in 2018

The schools of 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

[ slides ]

Irrelevance, independence and coherence

Presented by G. de Cooman at the SIPTA School in 2012

[ slides ]

Structural judgements

Presented by G. de Cooman at the SIPTA School in 2010

The school of 2008 also covered this topic.

**Particular models**

Belief functions

Presented by S. Destercke at the SIPTA School in 2018

Non additive measures

Presented by I. Couso & D. Dubois at the SIPTA School in 2014

[ slides ]

Coherent conditional lower previsions

Presented by E. Miranda at the SIPTA School in 2012

[ slides ]

Sets of desirable gambles

Presented by E. Quaeghebeur at the SIPTA School in 2010

**Decision making**

Decision making

Presented by T. Seidenfeld at the SIPTA School in 2022

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

Decision making with IP

Presented by M. Troffaes at the SIPTA School in 2018

[ slides ] [ solutions.r ] [ classification.r ] [ improb-redux.r ]

Preferences and choice functions

Presented by T. Seidenfeld at the SIPTA School in 2012

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

**Graphical models and credal networks**

Credal nets, probabilistic circuits and generative random forests

Presented by C. de Campo at the SIPTA School in 2022

[ slides 1 ] [ slides 2 ] [ video ] [ examples ]

Credal networks

Presented by F. Cozman & D. Mauá at the SIPTA School in 2020

[ slides ] [ video 1 ] [ video 2 ]

Graphical models

Presented by A. Antonucci, C. de Campos & F. Mangili at the SIPTA School in 2014

[ slides ]

Credal trees under epistemic irrelevance

Presented by G. de Cooman at the SIPTA School in 2012

[ slides ]

The schools of 2016, 2014, 2010 and 2004 also covered this topic.

**Machine learning and classification**

Machine learning with IP

Presented by C. de Campos at the SIPTA School in 2018

Classification

Presented by A. Antonucci at the SIPTA School in 2012

[ slides ]

Classification

Presented by C. de Campos, A. Antonucci & G. Corani at the SIPTA School in 2010

**Statistics and predictive inference**

Statistics and imprecise probabilities

Presented by T. Augustin at the SIPTA School in 2022

[ slides ] [ video 1 ] [ video 2 ]

Game-theoretic foundations for statistical testing and imprecise probabilities

Presented by G. Shafer at the SIPTA School in 2020

[ slides 1 ] [ video 1 ] [ slides 2 ] [ video 2 ]

Inferential models

Presented by R. Martin at the SIPTA School in 2020

[ slides ] [ video 1 ] [ video 2 ]

Robust Bayesian statistics and reliability networks

Presented by G. Walter at the SIPTA School in 2016

[ slides ]

Predictive inference

Presented by E. Quaeghebeur & G. de Cooman at the SIPTA School in 2014

[ slides ] [ Poisson ] [ binomial ] [ symmetry ] [ exchangeability ]

Bayes linear statistics

Presented by J. Cumming & I. Vernon at the SIPTA School in 2010

[ slides ] [ exercises ] [ solutions ]

Nonparametric predictive inference

Presented by F. Coolen & T. Coolen-Maturi at the SIPTA School in 2010

**Imprecise Markov chains**

Markov Decision Processes with Imprecise Probabilities (MDPIPs)

Presented by F. Cozman at the SIPTA School in 2022

Queueing systems

Presented by G. de Cooman & F. Hermans at the SIPTA School in 2012

[ slides ]

State sequence estimation in imprecise hidden Markov models

Presented by J. De Bock at the SIPTA School in 2012

[ slides ]

Imprecise Markov chains

Presented by D. Škulj at the SIPTA School in 2010

**Applications**

Engineering

Presented by S. Ferson at the SIPTA School in 2018

[ slides ]

Environmental applications

Presented by U. Sahlin at the SIPTA School in 2016

Engineering applications

Presented by E. Patelli at the SIPTA School in 2016

[ slides ]

Climate change applications

Presented by H. Held at the SIPTA School in 2014

[ slides ]

Earthquake rate prediction

Presented by A. Van Camp & G. de Cooman at the SIPTA School in 2012

[ slides ]

Correcting mistakes of OCR software

Presented by J. De Bock at the SIPTA School in 2012

[ slides ]

Environmental and military applications

Presented by A. Antonucci & M. Zaffalon at the SIPTA School in 2008

[ slides ]

**Other topics**

Accuracy for imprecise probabilities

Presented by J. Konek & B. Levinstein at the SIPTA School in 2022

[ slides 1 ] [ slides 2 ] [ slides 3 ] [ video 1 ] [ video 2 ] [ video 3 ] [ IP_Loss.ipynb ] [ Spherical_loss.ipynb ]

Probabilistic logic, programming and argumentation

Presented by F. Cozman at the SIPTA School in 2022

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

Expert Aggregation

Presented by S. Bradley at the SIPTA School in 2020

[ slides 1 ] [ slides 2 ] [ video ]

Risk analysis

Presented by D. Dubois at the SIPTA School in 2012

[ slides ]

Game theoretic probability

Presented by G. Shafer at the SIPTA School in 2008

[ slides ]