| Title: |
Analytic weak-signal approximation of the Bayes factor for continuous gravitational waves |
| Authors: |
Prix, R. |
| Source: |
Classical and Quantum Gravity |
| Publication Year: |
2025 |
| Collection: |
Max Planck Society: MPG.PuRe |
| Description: |
We generalize the targeted $\mathcal{B}$-statistic for continuous gravitational waves by modeling the $h_0$-prior as a half-Gaussian distribution with scale parameter $H$. This approach retains analytic tractability for two of the four amplitude marginalization integrals and recovers the standard $\mathcal{B}$-statistic in the strong-signal limit ($H\rightarrow\infty$). By Taylor-expanding the weak-signal regime ($H\rightarrow0$), the new prior enables fully analytic amplitude marginalization, resulting in a simple, explicit statistic that is as computationally efficient as the maximum-likelihood $\mathcal{F}$-statistic, but significantly more robust. Numerical tests show that for day-long coherent searches, the weak-signal Bayes factor achieves sensitivities comparable to the $\mathcal{F}$-statistic, though marginally lower than the standard $\mathcal{B}$-statistic (and the Bero-Whelan approximation). In semi-coherent searches over short (compared to a day) segments, this approximation matches or outperforms the weighted dominant-response $\mathcal{F}_{\mathrm{ABw}}$-statistic and returns to the sensitivity of the (weighted) $\mathcal{F}_{\mathrm{w}}$-statistic for longer segments. Overall the new Bayes-factor approximation demonstrates state-of-the-art or improved sensitivity across a wide range of segment lengths we tested (from 900s to 10days). |
| Document Type: |
article in journal/newspaper |
| File Description: |
application/pdf |
| Language: |
unknown |
| Relation: |
info:eu-repo/semantics/altIdentifier/arxiv/2409.13069 |
| Availability: |
https://hdl.handle.net/21.11116/0000-000F-DFCF-E; https://hdl.handle.net/21.11116/0000-000F-DFD1-A; https://hdl.handle.net/21.11116/0000-0010-CA30-4 |
| Rights: |
info:eu-repo/semantics/openAccess ; http://creativecommons.org/licenses/by/4.0/ |
| Accession Number: |
edsbas.96F3F9BE |
| Database: |
BASE |