Testing the statistical compatibility of data sets with a common prior
Abstract
The Parameter Goodness-of-fit (PG) test [hep-ph/0304176] offers a simple test statistic to study the compatibility of different data sets within a given theoretical model. In its original formulation it assumes that the data sets are statistically independent. We propose an extension of the PG test for the situation when some parameters of the model are constrained by an auxiliary data set called prior here. As the prior is imposed for all data sets, they are no longer statistically independent. We show that under the Gaussian approximation, the prior-constrained PG test statistic follows a generalised χ2 distribution, which can be used to obtain p-values in a straight-forward way. In the approximation of a strong prior constraint, the test converges towards the standard PG test for the unconstrained model parameters.
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BibTeX
@misc{coloma2026testing,
title = {{Testing the statistical compatibility of data sets with a common prior}},
author = {Pilar Coloma and Michele Maltoni and Thomas Schwetz},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28681},
eprint = {2610.28681},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28681},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Testing the statistical compatibility of data sets with a common prior
AU - Pilar Coloma
AU - Michele Maltoni
AU - Thomas Schwetz
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.28681
UR - https://arxiv.org/abs/2610.28681
AB - The Parameter Goodness-of-fit (PG) test [hep-ph/0304176] offers a simple test statistic to study the compatibility of different data sets within a given theoretical model. In its original formulation it assumes that the data sets are statistically independent. We propose an extension of the PG test for the situation when some parameters of the model are constrained by an auxiliary data set called prior here. As the prior is imposed for all data sets, they are no longer statistically independent. We show that under the Gaussian approximation, the prior-constrained PG test statistic follows a generalised χ^2 distribution, which can be used to obtain p-values in a straight-forward way. In the approximation of a strong prior constraint, the test converges towards the standard PG test for the unconstrained model parameters.
ER -