Title: Nonparametric predictive inference for multiple future ordinal observations
Authors: Abdulmajeed Alharbi - Durham University (United Kingdom) [presenting]
Abstract: In the theory of classical probability, a single precise probability satisfying Kolmogorov's axioms is used to quantify uncertainty. Imprecise probability in uncertainty quantification constitutes an appropriate and more general alternative approach when the information is incomplete or vague. Nonparametric Predictive Inference (NPI) is one of the statistical methodologies that have been developed to quantify uncertainty using imprecise probabilities, and it is based only on an exchangeability assumption for future and past observations. NPI has been developed for ordinal data, which are a type of categorical data with ordered categories. Examples of such data include pain level, satisfaction rating and education level. NPI methods for ordinal data use an assumed underlying data representation, with latent variables on the real-line falling into intervals which represent the categories. NPI for ordinal data was developed with attention restricted to a single future observation; our aim is to generalise this to multiple future observations and develop statistical methods based on this. Lower and upper probabilities for events involving multiple ordinal future observations are presented. This development forms the basis for a range of possible applications to be considered later, such as an application to the reproducibility of statistical tests for ordinal data.