On the calculation of p-values for quadratic statistics in Pulsar Timing Arrays
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911392719699968 |
|---|---|
| author | van Haasteren, Rutger |
| author_facet | van Haasteren, Rutger |
| contents | Pulsar Timing Array (PTA) projects have reported various lines of evidence suggesting the presence of a stochastic gravitational wave (GW) background in their data. One key line of evidence involves a detection statistic sensitive to inter-pulsar correlations, such as those induced by GWs. A $p$-value is then calculated to assess how unlikely it is for the observed signal to arise under the null hypothesis $H_0$, purely by chance. However, PTAs cannot empirically draw samples from $H_0$. As a workaround, various techniques are used in the literature to approximate $p$-values under $H_0$. One such technique, which has been heralded as a model-independent method, is the use of "scrambling" transformations that modify the data to cancel out pulsar correlations, thereby simulating realizations from $H_0$. In this work, scrambling methods and the detection statistic are investigated from first principles. The $p$-value methodology that is discussed is general, but the discussions regarding a specific detection statistic apply to the detection of a stochastic background of gravitational waves with PTAs. All methods in the literature to calculate $p$-values for such a detection statistic are rigorously analyzed, and many analytical expressions are derived. All this leads to the conclusion that scrambling methods are not model-independent and thus not completely empirical. Rigorous Bayesian and Frequentist $p$-value calculation methods are advocated, the evaluation of which depend on the generalized $χ^2$ distribution. This view is consistent with the posterior predictive $p$-value approach that is already in the literature. Efficient expressions are derived to evaluate the generalized $χ^2$ distribution of the detection statistic on real data. It is highlighted that no Frequentist $p$-values have been calculated correctly in the PTA literature to date. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_10811 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the calculation of p-values for quadratic statistics in Pulsar Timing Arrays van Haasteren, Rutger Instrumentation and Methods for Astrophysics General Relativity and Quantum Cosmology Pulsar Timing Array (PTA) projects have reported various lines of evidence suggesting the presence of a stochastic gravitational wave (GW) background in their data. One key line of evidence involves a detection statistic sensitive to inter-pulsar correlations, such as those induced by GWs. A $p$-value is then calculated to assess how unlikely it is for the observed signal to arise under the null hypothesis $H_0$, purely by chance. However, PTAs cannot empirically draw samples from $H_0$. As a workaround, various techniques are used in the literature to approximate $p$-values under $H_0$. One such technique, which has been heralded as a model-independent method, is the use of "scrambling" transformations that modify the data to cancel out pulsar correlations, thereby simulating realizations from $H_0$. In this work, scrambling methods and the detection statistic are investigated from first principles. The $p$-value methodology that is discussed is general, but the discussions regarding a specific detection statistic apply to the detection of a stochastic background of gravitational waves with PTAs. All methods in the literature to calculate $p$-values for such a detection statistic are rigorously analyzed, and many analytical expressions are derived. All this leads to the conclusion that scrambling methods are not model-independent and thus not completely empirical. Rigorous Bayesian and Frequentist $p$-value calculation methods are advocated, the evaluation of which depend on the generalized $χ^2$ distribution. This view is consistent with the posterior predictive $p$-value approach that is already in the literature. Efficient expressions are derived to evaluate the generalized $χ^2$ distribution of the detection statistic on real data. It is highlighted that no Frequentist $p$-values have been calculated correctly in the PTA literature to date. |
| title | On the calculation of p-values for quadratic statistics in Pulsar Timing Arrays |
| topic | Instrumentation and Methods for Astrophysics General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2506.10811 |