Imprecision Attenuates Updating
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909767756152832 |
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| author | Vaeth, Martin |
| author_facet | Vaeth, Martin |
| contents | This paper studies how imprecision in noisy signals attenuates Bayesian updating toward the prior. This phenomenon is well-known under a normal prior and normal noise, where less precise signals yield posterior means closer to the prior mean. We show this effect extends to any symmetric, log-concave prior and any symmetric, quasi-concave location experiment, using a newly introduced precision order. Our main result is that for any such prior and any signal realization, the posterior mean under location experiment S is closer to the prior mean than is the posterior mean under S', if and only if S is less precise than S'. We discuss applications to cognitive imprecision, prior precision, and overconfidence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02238 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Imprecision Attenuates Updating Vaeth, Martin Theoretical Economics This paper studies how imprecision in noisy signals attenuates Bayesian updating toward the prior. This phenomenon is well-known under a normal prior and normal noise, where less precise signals yield posterior means closer to the prior mean. We show this effect extends to any symmetric, log-concave prior and any symmetric, quasi-concave location experiment, using a newly introduced precision order. Our main result is that for any such prior and any signal realization, the posterior mean under location experiment S is closer to the prior mean than is the posterior mean under S', if and only if S is less precise than S'. We discuss applications to cognitive imprecision, prior precision, and overconfidence. |
| title | Imprecision Attenuates Updating |
| topic | Theoretical Economics |
| url | https://arxiv.org/abs/2504.02238 |