Bernoulli's golden theorem in retrospect: error probabilities and trustworthy evidence.
Bernoulli's 1713 golden theorem is viewed retrospectively in the context of modern model-based frequentist inference that revolves around the concept of a prespecified statistical model M θ x , defining the inductive premises of inference. It is argued that several widely-accepted claims relating to...
| Publicado en: | Synthese Vol. 199; no. 5/6; pp. 13949 - 13977 |
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| Formato: | Artículo |
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Springer Nature
Dec2021
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| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=154480443&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 154480443 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00397857 4LI jtl: Synthese issn: 00397857 maglogo: N pubinfo: dt: Dec2021 vid: 199 iid: 5/6 pid: 237 pub: Springer Nature artinfo: ui: 154480443 10.1007/s11229-021-03405-z ppf: 13949 ppct: 28 formats: fmt: @attributes: type: P size: 563KB tig: atl: Bernoulli's golden theorem in retrospect: error probabilities and trustworthy evidence. aug: au: Spanos, Aris affil: Department of Economics, Virginia Tech, 24061, Blacksburg, VA, USA su: Frequentist statistics Random variables Law of large numbers Statistical models Inverse problems Probability theory sug: subj: Frequentist statistics Random variables Law of large numbers Statistical models Inverse problems Probability theory keyword: Bayes' rule Bernoulli's golden theorem Bernoulli's swindle Direct versus inverse inference Effect sizes Error probabilities Factual versus hypothetical reasoning p Value Straight rule ab: Bernoulli's 1713 golden theorem is viewed retrospectively in the context of modern model-based frequentist inference that revolves around the concept of a prespecified statistical model M θ x , defining the inductive premises of inference. It is argued that several widely-accepted claims relating to the golden theorem and frequentist inference are either misleading or erroneous: (a) Bernoulli solved the problem of inference 'from probability to frequency', and thus (b) the golden theorem cannot justify an approximate Confidence Interval (CI) for the unknown parameter θ , (c) Bernoulli identified the probability P A with the relative frequency 1 n ∑ k = 1 n x k of event A as a result of conflating f (x 0 | θ) with f (θ | x 0) , where x 0 denotes the observed data, and (d) the same 'swindle' is currently perpetrated by the p value testers. In interrogating the claims (a)–(d), the paper raises several foundational issues that are particularly relevant for statistical induction as it relates to the current discussions on the replication crises and the trustworthiness of empirical evidence, arguing that: [i] The alleged Bernoulli swindle is grounded in the unwarranted claim θ ^ n x 0 ≃ θ ∗ , for a large enough n, where θ ^ n X is an optimal estimator of the true value θ ∗ of θ. [ii] Frequentist error probabilities are not conditional on hypotheses (H and H) framed in terms of an unknown parameter θ since θ is neither a random variable nor an event. [iii] The direct versus inverse inference problem is a contrived and misplaced charge since neither conditional distribution f (x 0 | θ) and f (θ | x 0) exists (formally or logically) in model-based ( M θ x ) frequentist inference. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Synthese is a copyright of Springer, 2021. All Rights Reserved. item: Synthese holder: Springer Nature dt: @attributes: year: 2021 holdings: @attributes: islocal: N |
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