Optimal Statistic : A method for Gravitational Wave Background search analysis

Detection of a low-frequency stochastic gravitational wave background (GWB) can be achieved using the Pulsar Timing Array (PTA) technique, which leverages the high-precision timing of millisecond pulsars. By analyzing the timing residuals of these pulsars, we can extract signatures of the GWB. There are mainly two types of methods to analyze data : (1) Bayesian inference method (2) frequentist inference method. PTAs uses a hybrid Bayesian-frequentist approach that provides an efficient framework for data analysis which is known as Optimal Statistic. The method employs an estimator to determine the signal-to-noise ratio (S/N) and the amplitude of the GWB while fixing the spectral index. An optimal filter is then applied to optimize the signal to noise ratio (S/N) and amplitude estimation.Also it provides an Hellings And Downs (HD) correlation curve for GWB signal. Compared to fully Bayesian approaches, this method offers significant advantages in computational efficiency and speed, making it an ideal tool for large-scale pulsar datasets. I intend to present the Optimal Statistic Method which is useful for the GWB search analysis .