Abstract
Abstract Based on observations of real-valued random quantities from k⩾2 independent sources, new results are presented on bounds for predictive probabilities for further unknown random quantities from each source. Past and future observations per source are related via the assumption A(n) (Hill, J. Amer. Statist. Assoc. 63 (1968) 677), which is closely linked to finite exchangeability. Attention is particularly focussed on the question: which source will provide the largest next observation, when taking one more observation from each source? Our approach enables a nonparametric predictive comparison between the sources, which might naturally be linked to choices between sources, leading us to suggest our method as an alternative formulation to classical selection approaches and to introduce the term ‘imprecise predictive selection’. We present imprecise predictive selection of a single best source and of a subset of m (m⩽k−1) sources. We consider two cases for selection of a subset, namely a subset that contains the m best sources, and a subset that is just required to include the single best source. We also briefly present a related approach, using imprecise previsions with an interpretation as bounds for expected values for future observations.
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