Incompletely Known Sample Spaces: Models and Human Intuitions

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Michael Smithson ;
Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, PMLR 103:367-376, 2019.

Abstract

This paper surveys models and human intuitions about incompletely known “sample spaces” ($\Omega$). Given that there are very few guidelines for how best to form such beliefs when $\Omega$ is incompletely known, and there is very little research on the psychology behind beliefs about $\Omega$, this survey is preliminary and brings in ideas and models from probability and statistics, biology, and psychology. Pilot experimental studies of how people estimate the cardinality of $\Omega$ when given sample information from it are presented, demonstrating that to a surprising extent their estimates correspond with those produced by normative statistical models. The paper concludes by outlining future directions for a research program on this topic.

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