Two sides of the same coin: the F-statistic and the 5-vector method

Abstract

This work explores the relationship between two data-analysis methods used in the search for continuous gravitational waves in LIGO-Virgo-KAGRA data: the $\mathcal{F}$-statistic and the 5-vector method. We show that the 5-vector method can be derived from a maximum likelihood framework similar to the $\mathcal{F}$-statistic. Our analysis demonstrates that the two methods are statistically equivalent, providing the same detection probability for a given false alarm rate. We extend this comparison to multiple detectors, highlighting differences from the standard approach that simply combines 5-vectors from each detector. In our maximum likelihood approach, each 5-vector is weighted by the observation time and sensitivity of its respective detector, resulting in efficient estimators and analytical distributions for the detection statistic. Additionally, we present the analytical computation of sensitivity for different searches, expressed in terms of the minimum detectable amplitude.

References in corpus (23)

• Advanced Virgo: a 2nd generation interferometric gravitational wave detector
• Advanced LIGO
• Detector configuration of KAGRA - the Japanese cryogenic gravitational-wave detector
• Data analysis of gravitational-wave signals from spinning neutron stars. I. The signal and its detection
• The generalized F-statistic: multiple detectors and multiple GW pulsars
• The search for continuous gravitational waves: metric of the multi-detector F-statistic
• Searches for Gravitational Waves from Known Pulsars at Two Harmonics in 2015-2017 LIGO Data
• Optimal filtering of the LISA data
• Targeted search for continuous gravitational waves: Bayesian versus maximum-likelihood statistics
• Searches for Gravitational Waves from Known Pulsars at Two Harmonics in the Second and Third LIGO-Virgo Observing Runs
• Directed searches for continuous gravitational waves from binary systems: parameter-space metrics and optimal Scorpius X-1 sensitivity
• Status and perspectives of Continuous Gravitational Wave searches
• A new data analysis framework for the search of continuous gravitational wave signals
• A method for narrow-band searches of continuous gravitational wave signals
• Searching for gravitational waves from known pulsars using the $\mathcal{F}$ and $\mathcal{G}$ statistics
• Optimal Template Banks
• Coherent search of continuous gravitational wave signals: extension of the 5-vectors method to a network of detectors
• Banks of templates for all-sky narrow-band searches of gravitational waves from spinning neutron stars
• Banks of templates for directed searches of gravitational waves from spinning neutron stars
• Bayesian $\mathcal{F}$-statistic-based parameter estimation of continuous gravitational waves from known pulsars
• Search for gravitational wave signals from known pulsars in LIGO-Virgo O3 data using the 5n-vector ensemble method
• Phase decomposition of the template metric for continuous gravitational-wave searches
• Banks of templates for directed and all-sky narrow-band searches of continuous gravitational waves from spinning neutron stars with several spindowns

Cited by in corpus (5)

• Search for continuous gravitational waves from known pulsars in the first part of the fourth LIGO-Virgo-KAGRA observing run
• Search for continuous gravitational wave signals from luminous dark photon superradiance clouds with LVK O3 observations
• A directed continuous-wave search from Scorpius X-1 with the five-vector resampling technique
• Analytic weak-signal approximation of the Bayes factor for continuous gravitational waves
• Narrowband searches for continuous gravitational waves from known pulsars in the first two parts of the fourth LIGO--Virgo--KAGRA observing run