From <i>p</i>-Values to Posterior Probabilities of Null Hypotheses
Minimum Bayes factors are commonly used to transform two-sided <i>p</i>-values to lower bounds on the posterior probability of the null hypothesis, in particular the bound <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">&l...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-04-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/25/4/618 |
| _version_ | 1797605607912505344 |
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| author | Daiver Vélez Ramos Luis R. Pericchi Guerra María Eglée Pérez Hernández |
| author_facet | Daiver Vélez Ramos Luis R. Pericchi Guerra María Eglée Pérez Hernández |
| author_sort | Daiver Vélez Ramos |
| collection | DOAJ |
| description | Minimum Bayes factors are commonly used to transform two-sided <i>p</i>-values to lower bounds on the posterior probability of the null hypothesis, in particular the bound <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>−</mo><mi>e</mi><mo>·</mo><mi>p</mi><mo>·</mo><mo form="prefix">log</mo><mo>(</mo><mi>p</mi><mo>)</mo></mrow></semantics></math></inline-formula>. This bound is easy to compute and explain; however, it does not behave as a Bayes factor. For example, it does not change with the sample size. This is a very serious defect, particularly for moderate to large sample sizes, which is precisely the situation in which <i>p</i>-values are the most problematic. In this article, we propose adjusting this minimum Bayes factor with the information to approximate an exact Bayes factor, not only when <i>p</i> is a <i>p</i>-value but also when <i>p</i> is a pseudo-<i>p</i>-value. Additionally, we develop a version of the adjustment for linear models using the recent refinement of the Prior-Based BIC. |
| first_indexed | 2024-03-11T05:03:29Z |
| format | Article |
| id | doaj.art-ceaf28dacccd412aa4d50107947eeb4c |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-11T05:03:29Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-ceaf28dacccd412aa4d50107947eeb4c2023-11-17T19:08:37ZengMDPI AGEntropy1099-43002023-04-0125461810.3390/e25040618From <i>p</i>-Values to Posterior Probabilities of Null HypothesesDaiver Vélez Ramos0Luis R. Pericchi Guerra1María Eglée Pérez Hernández2Faculty of Business Administration, Statistical Institute and Computerized Information Systems, Río Piedras Campus, University of Puerto Rico, 15 AVE Universidad STE 1501, San Juan, PR 00925-2535, USAFaculty of Natural Sciences, Department of Mathematics, Río Piedras Campus, University of Puerto Rico, 17 AVE Universidad STE 1701, San Juan, PR 00925-2537, USAFaculty of Natural Sciences, Department of Mathematics, Río Piedras Campus, University of Puerto Rico, 17 AVE Universidad STE 1701, San Juan, PR 00925-2537, USAMinimum Bayes factors are commonly used to transform two-sided <i>p</i>-values to lower bounds on the posterior probability of the null hypothesis, in particular the bound <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>−</mo><mi>e</mi><mo>·</mo><mi>p</mi><mo>·</mo><mo form="prefix">log</mo><mo>(</mo><mi>p</mi><mo>)</mo></mrow></semantics></math></inline-formula>. This bound is easy to compute and explain; however, it does not behave as a Bayes factor. For example, it does not change with the sample size. This is a very serious defect, particularly for moderate to large sample sizes, which is precisely the situation in which <i>p</i>-values are the most problematic. In this article, we propose adjusting this minimum Bayes factor with the information to approximate an exact Bayes factor, not only when <i>p</i> is a <i>p</i>-value but also when <i>p</i> is a pseudo-<i>p</i>-value. Additionally, we develop a version of the adjustment for linear models using the recent refinement of the Prior-Based BIC.https://www.mdpi.com/1099-4300/25/4/618<i>p</i>-value calibrationBayes factorlinear modelpseudo-p-valueadaptive levels |
| spellingShingle | Daiver Vélez Ramos Luis R. Pericchi Guerra María Eglée Pérez Hernández From <i>p</i>-Values to Posterior Probabilities of Null Hypotheses Entropy <i>p</i>-value calibration Bayes factor linear model pseudo-p-value adaptive levels |
| title | From <i>p</i>-Values to Posterior Probabilities of Null Hypotheses |
| title_full | From <i>p</i>-Values to Posterior Probabilities of Null Hypotheses |
| title_fullStr | From <i>p</i>-Values to Posterior Probabilities of Null Hypotheses |
| title_full_unstemmed | From <i>p</i>-Values to Posterior Probabilities of Null Hypotheses |
| title_short | From <i>p</i>-Values to Posterior Probabilities of Null Hypotheses |
| title_sort | from i p i values to posterior probabilities of null hypotheses |
| topic | <i>p</i>-value calibration Bayes factor linear model pseudo-p-value adaptive levels |
| url | https://www.mdpi.com/1099-4300/25/4/618 |
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