Imprecision Attenuates Updating

Martin Vaeth

Papers from arXiv.org

Abstract: 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.

Date: 2025-04, Revised 2025-04
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2504.02238

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