Posteriors in Limited Time
This paper obtains a measure-theoretic restriction that must be satisfied by a prior probability measure for posteriors to be computed in limited time. Specifically, it is shown that the prior must be factorizable. Factorizability is a set of independence conditions for events in the sample space th...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-12-01
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| Series: | AppliedMath |
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| Online Access: | https://www.mdpi.com/2673-9909/2/4/41 |
| _version_ | 1797461696433881088 |
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| author | Ayan Bhattacharya |
| author_facet | Ayan Bhattacharya |
| author_sort | Ayan Bhattacharya |
| collection | DOAJ |
| description | This paper obtains a measure-theoretic restriction that must be satisfied by a prior probability measure for posteriors to be computed in limited time. Specifically, it is shown that the prior must be factorizable. Factorizability is a set of independence conditions for events in the sample space that allows agents to calculate posteriors using only a subset of the dataset. The result has important implications for models in mathematical economics and finance that rely on a common prior. If one introduces the limited time restriction to Aumann’s famous <i>Agreeing to Disagree</i> setup, one sees that checking for factorizability requires agents to have access to every event in the measure space, thus severely limiting the scope of the agreement result. |
| first_indexed | 2024-03-09T17:23:02Z |
| format | Article |
| id | doaj.art-6dc8f098c9f141069ff03078750d732f |
| institution | Directory Open Access Journal |
| issn | 2673-9909 |
| language | English |
| last_indexed | 2024-03-09T17:23:02Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | AppliedMath |
| spelling | doaj.art-6dc8f098c9f141069ff03078750d732f2023-11-24T12:59:23ZengMDPI AGAppliedMath2673-99092022-12-012470071010.3390/appliedmath2040041Posteriors in Limited TimeAyan Bhattacharya0Booth School of Business, University of Chicago, Chicago, IL 60637, USAThis paper obtains a measure-theoretic restriction that must be satisfied by a prior probability measure for posteriors to be computed in limited time. Specifically, it is shown that the prior must be factorizable. Factorizability is a set of independence conditions for events in the sample space that allows agents to calculate posteriors using only a subset of the dataset. The result has important implications for models in mathematical economics and finance that rely on a common prior. If one introduces the limited time restriction to Aumann’s famous <i>Agreeing to Disagree</i> setup, one sees that checking for factorizability requires agents to have access to every event in the measure space, thus severely limiting the scope of the agreement result.https://www.mdpi.com/2673-9909/2/4/41limited timeBayesian inferenceprobabilistic independencebounded rationalityfactorizability |
| spellingShingle | Ayan Bhattacharya Posteriors in Limited Time AppliedMath limited time Bayesian inference probabilistic independence bounded rationality factorizability |
| title | Posteriors in Limited Time |
| title_full | Posteriors in Limited Time |
| title_fullStr | Posteriors in Limited Time |
| title_full_unstemmed | Posteriors in Limited Time |
| title_short | Posteriors in Limited Time |
| title_sort | posteriors in limited time |
| topic | limited time Bayesian inference probabilistic independence bounded rationality factorizability |
| url | https://www.mdpi.com/2673-9909/2/4/41 |
| work_keys_str_mv | AT ayanbhattacharya posteriorsinlimitedtime |