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” ($\Omega$). 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.

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 = {http://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 http://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 http://proceedings.mlr.press/v103/smithson19b.html.

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