2024/10/16 by Cook, A. M., Li, Dayi, Eadie, Gwendolyn M. +12
#Applications (stat.AP) #FOS: Computer and information sciences #FOS: Physical sciences #Instrumentation and Methods for Astrophysics (astro-ph.IM)
paper · doi:10.48550/arxiv.2410.12146
This paper introduces 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, we estimate hyperparameters governing a physically motivated NHPP intensity. Simulation studies demonstrate the reliability of this methodology in accurately estimating hyperparameters. Leveraging the posterior distribution, we then infer the probability of detecting a certain number of events within a given radius, the k-contact distance. We demonstrate our 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 in the detection domain, or the probability of coincidence (PC). The new methodology improves the repeater detection PC in 91% 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 ∼ 4800.