Statistical inference

This chapter introduces the use of imprecise probabilities in statistical inference. It first provides a sketch of the most important different inference concepts. Next, the chapter explains the different understandings and interpretations of imprecision in statistics, including an ideal typical distinction between model and data imprecision, and discusses some motives for the paradigmatic shift towards imprecise probabilities in statistics. Then, it describes the main inference concepts under model imprecision, namely generalized Bayesian inference. Selected aspects of the frequentist approach, the methodology of nonparametric predictive inference (NPI) along with other approaches are also mentioned in the chapter. The concept of partial identification as a framework for handling observationally equivalent models is explained. The chapter discusses some general challenges, before providing a guide for further reading.