Introduction to Imprecise Probabilities

Chapter 7Statistical inference

Thomas Augustin¹, Gero Walter¹, and Frank P. A. Coolen²

¹Department of Statistics, Ludwig-Maximilians University Munich (LMU), Germany

²Department of Mathematical Sciences, Durham University, UK

This chapter introduces the use of imprecise probabilities in statistical inference. In contrast to many other fields, in this area the development of methodology based on imprecise probabilities is still in its early stages. From the current perspective of statistical modelling, the procedures proposed so far are mostly rather basic, but even already there imprecise probabilities prove very powerful. By overcoming some fundamental limitations inherent in traditional statistics, imprecise probabilities are promising a comprehensive framework for reliable inference and data analysis.

With still so much to explore, statistical inference with imprecise probability offers excellent opportunities for research, and the authors hope to stimulate its advancement with this overview. To keep the material at an appropriate length, many choices had to be made in the presentation. Our major goal is to achieve an exemplary perception of the power of imprecise probability methods in the area of statistical inference, as well as to raise awareness of the many challenges still waiting. Therefore we often give up mathematical rigour in favour of an informal description aiming at an intuition of the basic concepts.¹

This chapter is organized as follows: Taking the heterogeneous ...