Quantifying the Clustering Probability in Noisy Nonhomogeneous Spatial Data to Identify New Repeating Fast Radio Burst Sources from CHIME/FRB

Music City Center 

In this paper, I introduce an approach to analyze nonhomogeneous Poisson processes (NHPP) observed with noise, focusing on previously unstudied second-order characteristics of the noisy process. Utilizing a hierarchical Bayesian model with noisy data, I estimate hyperparameters governing a physically motivated NHPP intensity. I perform simulation studies to demonstrate the reliability of this methodology in accurately estimating hyperparameters. Leveraging the posterior distribution, I then infer the probability of detecting a certain number of events within a given radius, the k-contact distance. I demonstrate the methodology with an application to observations of fast radio bursts (FRBs) detected by the Canadian Hydrogen Intensity Mapping Experiment's FRB Project (CHIME/FRB). This approach allows us to identify repeating FRB sources by bounding or directly simulating the probability of observing k physically independent sources within some radius, or the probability of coincidence (PC). The new methodology improves the repeater detection PC in 86% of cases when applied to the largest sample of previously classified observations, with a median improvement factor (existing metric over PC from our methodology) of ∼ 3000.