Chapter 2
Introduction to Imprecise Probabilities
Daniel Krpelík and Tathagata Basu
Abstract Since uncertainty is persistent in engineering analyses, this chapter aimed
to introduce methods to describe and reason with under uncertainty in various
scenarios. Probability theory is the most widely used methodology for uncertainty
quantification for a long time and has proven to be a powerful tool for this task.
Nevertheless, the construction of stochastic models relies on very fine information,
such as large amount of observations, which is not always available. Without it, the
constructed models are only very rough approximations of the real laws and may
cause incorrect decisions. In this chapter, we introduce other types of models, based
on the theory of imprecise probability, which we are able to construct and reason
with under situations with limited available knowledge.
Keywords Imprecise probability · Uncertainty · Lower previsions · Robust
inference
2.1 Introduction
The desired outcome of an engineering project is a system which provides the
service it was designed for. But the exact future behaviour of a system in the real
world is, ipso facto, unknown, until the system is built and tested. This also applies
to the use of familiar systems that operate under novel environmental conditions.
However, this poses a dilemma: how to design systems so that they meet our
requirements once deployed? Thus, we need some procedure(s) to help us with the
D. Krpelík ()
Department of Mathematical Sciences, Durham University, Durham, UK
Department of Applied Mathematics, VŠB - Technical University of Ostrava, Ostrava, Czechia
e-mail: daniel.krpelik@durham.ac.uk
T. Basu
Department of Mathematical Sciences, Durham University, Durham, UK
e-mail: tathagata.basu@durham.ac.uk
© Springer Nature Switzerland AG 2021
M. Vasile (ed.), Optimization Under Uncertainty with Applications to Aerospace
Engineering, https://doi.org/10.1007/978-3-030-60166-9_2
35
Introduction to Imprecise Probabilities
Daniel Krpelík and Tathagata Basu
Abstract Since uncertainty is persistent in engineering analyses, this chapter aimed
to introduce methods to describe and reason with under uncertainty in various
scenarios. Probability theory is the most widely used methodology for uncertainty
quantification for a long time and has proven to be a powerful tool for this task.
Nevertheless, the construction of stochastic models relies on very fine information,
such as large amount of observations, which is not always available. Without it, the
constructed models are only very rough approximations of the real laws and may
cause incorrect decisions. In this chapter, we introduce other types of models, based
on the theory of imprecise probability, which we are able to construct and reason
with under situations with limited available knowledge.
Keywords Imprecise probability · Uncertainty · Lower previsions · Robust
inference
2.1 Introduction
The desired outcome of an engineering project is a system which provides the
service it was designed for. But the exact future behaviour of a system in the real
world is, ipso facto, unknown, until the system is built and tested. This also applies
to the use of familiar systems that operate under novel environmental conditions.
However, this poses a dilemma: how to design systems so that they meet our
requirements once deployed? Thus, we need some procedure(s) to help us with the
D. Krpelík ()
Department of Mathematical Sciences, Durham University, Durham, UK
Department of Applied Mathematics, VŠB - Technical University of Ostrava, Ostrava, Czechia
e-mail: daniel.krpelik@durham.ac.uk
T. Basu
Department of Mathematical Sciences, Durham University, Durham, UK
e-mail: tathagata.basu@durham.ac.uk
© Springer Nature Switzerland AG 2021
M. Vasile (ed.), Optimization Under Uncertainty with Applications to Aerospace
Engineering, https://doi.org/10.1007/978-3-030-60166-9_2
35