A new calibrated bayesian internal goodness-of-fit method: sampled posterior p-values as simple and general p-values that allow double use of the data.

A new calibrated bayesian internal goodness-of-fit method: sampled posterior p-values as simple and general p-values that allow double use of the data.

BACKGROUND: Recent approaches mixing frequentist principles with bayesian inference propose internal goodness-of-fit (GOF) p-values that might be valuable for critical analysis of bayesian statistical models. However, GOF p-values developed to date only have known probability distributions under res...

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Main Author: Frédéric Gosselin
Format: Article
Language:English
Published: Public Library of Science (PLoS) 2011-01-01
Series:PLoS ONE
Online Access:http://europepmc.org/articles/PMC3060804?pdf=render
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spelling doaj-2c4e0799488b4d69a033a9f8374379272020-11-25T02:15:41ZengPublic Library of Science (PLoS)PLoS ONE1932-62032011-01-0163e1477010.1371/journal.pone.0014770A new calibrated bayesian internal goodness-of-fit method: sampled posterior p-values as simple and general p-values that allow double use of the data.Frédéric GosselinBACKGROUND: Recent approaches mixing frequentist principles with bayesian inference propose internal goodness-of-fit (GOF) p-values that might be valuable for critical analysis of bayesian statistical models. However, GOF p-values developed to date only have known probability distributions under restrictive conditions. As a result, no known GOF p-value has a known probability distribution for any discrepancy function. METHODOLOGY/PRINCIPAL FINDINGS: We show mathematically that a new GOF p-value, called the sampled posterior p-value (SPP), asymptotically has a uniform probability distribution whatever the discrepancy function. In a moderate finite sample context, simulations also showed that the SPP appears stable to relatively uninformative misspecifications of the prior distribution. CONCLUSIONS/SIGNIFICANCE: These reasons, together with its numerical simplicity, make the SPP a better canonical GOF p-value than existing GOF p-values.http://europepmc.org/articles/PMC3060804?pdf=render
collection DOAJ
language English
format Article
sources DOAJ
author Frédéric Gosselin
spellingShingle Frédéric Gosselin
A new calibrated bayesian internal goodness-of-fit method: sampled posterior p-values as simple and general p-values that allow double use of the data.
PLoS ONE
author_facet Frédéric Gosselin
author_sort Frédéric Gosselin
title A new calibrated bayesian internal goodness-of-fit method: sampled posterior p-values as simple and general p-values that allow double use of the data.
title_short A new calibrated bayesian internal goodness-of-fit method: sampled posterior p-values as simple and general p-values that allow double use of the data.
title_full A new calibrated bayesian internal goodness-of-fit method: sampled posterior p-values as simple and general p-values that allow double use of the data.
title_fullStr A new calibrated bayesian internal goodness-of-fit method: sampled posterior p-values as simple and general p-values that allow double use of the data.
title_full_unstemmed A new calibrated bayesian internal goodness-of-fit method: sampled posterior p-values as simple and general p-values that allow double use of the data.
title_sort new calibrated bayesian internal goodness-of-fit method: sampled posterior p-values as simple and general p-values that allow double use of the data.
publisher Public Library of Science (PLoS)
series PLoS ONE
issn 1932-6203
publishDate 2011-01-01
description BACKGROUND: Recent approaches mixing frequentist principles with bayesian inference propose internal goodness-of-fit (GOF) p-values that might be valuable for critical analysis of bayesian statistical models. However, GOF p-values developed to date only have known probability distributions under restrictive conditions. As a result, no known GOF p-value has a known probability distribution for any discrepancy function. METHODOLOGY/PRINCIPAL FINDINGS: We show mathematically that a new GOF p-value, called the sampled posterior p-value (SPP), asymptotically has a uniform probability distribution whatever the discrepancy function. In a moderate finite sample context, simulations also showed that the SPP appears stable to relatively uninformative misspecifications of the prior distribution. CONCLUSIONS/SIGNIFICANCE: These reasons, together with its numerical simplicity, make the SPP a better canonical GOF p-value than existing GOF p-values.
url http://europepmc.org/articles/PMC3060804?pdf=render
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