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Article: Demystify Lindley’s paradox by connecting p-value and posterior probability
Title | Demystify Lindley’s paradox by connecting p-value and posterior probability |
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Authors | |
Keywords | Bayesian posterior probability hypothesis testing Interpretation of p-value point null hypothesis two-sided test |
Issue Date | 2021 |
Publisher | International Press. The Journal's web site is located at http://www.intlpress.com/SII |
Citation | Statistics and its Interface, 2021, v. 14 n. 4, p. 489-502 How to Cite? |
Abstract | In the hypothesis testing framework, p‑value is often computed to determine whether to reject the null hypothesis or not. On the other hand, Bayesian approaches typically compute the posterior probability of the null hypothesis to evaluate its plausibility. We revisit Lindley’s paradox and demystify the conflicting results between Bayesian and frequentist hypothesis testing procedures by casting a two-sided hypothesis as a combination of two one-sided hypotheses along the opposite directions. This formulation can naturally circumvent the ambiguities of assigning a point mass to the null and choices of using local or non-local prior distributions. As p‑value solely depends on the observed data without incorporating any prior information, we consider non-informative prior distributions for fair comparisons with p‑value. The equivalence of p‑value and the Bayesian posterior probability of the null hypothesis can be established to reconcile Lindley’s paradox. More complicated settings, such as multivariate cases, random effects models and non-normal data, are also explored for generalization of our results to various hypothesis tests. |
Persistent Identifier | http://hdl.handle.net/10722/304013 |
ISSN | 2021 Impact Factor: 0.716 2020 SCImago Journal Rankings: 0.388 |
DC Field | Value | Language |
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dc.contributor.author | Yin, G | - |
dc.contributor.author | Shi, H | - |
dc.date.accessioned | 2021-09-23T08:54:01Z | - |
dc.date.available | 2021-09-23T08:54:01Z | - |
dc.date.issued | 2021 | - |
dc.identifier.citation | Statistics and its Interface, 2021, v. 14 n. 4, p. 489-502 | - |
dc.identifier.issn | 1938-7989 | - |
dc.identifier.uri | http://hdl.handle.net/10722/304013 | - |
dc.description.abstract | In the hypothesis testing framework, p‑value is often computed to determine whether to reject the null hypothesis or not. On the other hand, Bayesian approaches typically compute the posterior probability of the null hypothesis to evaluate its plausibility. We revisit Lindley’s paradox and demystify the conflicting results between Bayesian and frequentist hypothesis testing procedures by casting a two-sided hypothesis as a combination of two one-sided hypotheses along the opposite directions. This formulation can naturally circumvent the ambiguities of assigning a point mass to the null and choices of using local or non-local prior distributions. As p‑value solely depends on the observed data without incorporating any prior information, we consider non-informative prior distributions for fair comparisons with p‑value. The equivalence of p‑value and the Bayesian posterior probability of the null hypothesis can be established to reconcile Lindley’s paradox. More complicated settings, such as multivariate cases, random effects models and non-normal data, are also explored for generalization of our results to various hypothesis tests. | - |
dc.language | eng | - |
dc.publisher | International Press. The Journal's web site is located at http://www.intlpress.com/SII | - |
dc.relation.ispartof | Statistics and its Interface | - |
dc.rights | Statistics and its Interface. Copyright © International Press. | - |
dc.subject | Bayesian posterior probability | - |
dc.subject | hypothesis testing | - |
dc.subject | Interpretation of p-value | - |
dc.subject | point null hypothesis | - |
dc.subject | two-sided test | - |
dc.title | Demystify Lindley’s paradox by connecting p-value and posterior probability | - |
dc.type | Article | - |
dc.identifier.email | Yin, G: gyin@hku.hk | - |
dc.identifier.authority | Yin, G=rp00831 | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.4310/21-SII668 | - |
dc.identifier.hkuros | 325319 | - |
dc.identifier.volume | 14 | - |
dc.identifier.issue | 4 | - |
dc.identifier.spage | 489 | - |
dc.identifier.epage | 502 | - |
dc.publisher.place | United States | - |