Incompletely Known Sample Spaces: Models and Human Intuitions

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” (Ω). Given that there are very few guidelines for how best to form such beliefs when Ω is incompletely known, and there is very little research on the psychology behind beliefs about Ω, 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 Ω 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v103-smithson19b, title = {Incompletely Known Sample Spaces: Models and Human Intuitions}, author = {Smithson, Michael}, booktitle = {Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications}, pages = {367--376}, year = {2019}, editor = {De Bock, Jasper and de Campos, Cassio P. and de Cooman, Gert and Quaeghebeur, Erik and Wheeler, Gregory}, volume = {103}, series = {Proceedings of Machine Learning Research}, month = {03--06 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v103/smithson19b/smithson19b.pdf}, url = {https://proceedings.mlr.press/v103/smithson19b.html}, 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.} }
Endnote
%0 Conference Paper %T Incompletely Known Sample Spaces: Models and Human Intuitions %A Michael Smithson %B Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications %C Proceedings of Machine Learning Research %D 2019 %E Jasper De Bock %E Cassio P. de Campos %E Gert de Cooman %E Erik Quaeghebeur %E Gregory Wheeler %F pmlr-v103-smithson19b %I PMLR %P 367--376 %U https://proceedings.mlr.press/v103/smithson19b.html %V 103 %X 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.
APA
Smithson, M.. (2019). Incompletely Known Sample Spaces: Models and Human Intuitions. Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, in Proceedings of Machine Learning Research 103:367-376 Available from https://proceedings.mlr.press/v103/smithson19b.html.

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