K-Contact Distance for Noisy Nonhomogeneous Spatial Point Data with application to Repeating Fast Radio Burst sources

TL;DR

This paper develops a Bayesian method to analyze noisy nonhomogeneous Poisson processes, enabling improved detection of repeating fast radio burst sources by estimating the probability of coincident events within a given radius.

Contribution

It introduces a hierarchical Bayesian framework for second-order analysis of noisy NHPP data, specifically applied to identifying repeating FRB sources, with significant improvements over existing methods.

Findings

Method accurately estimates hyperparameters in simulations

Increases repeater detection probability in 91% of cases

Median improvement factor of ~4800 over previous metrics

Abstract

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 $\textit{probability of coincidence}$ ($P_{\text{C}}$). The new methodology improves the repeater detection $P_{\text{C}}$ in 91% of cases when applied to the largest sample of previously classified observations, with a median improvement factor (existing metric over $P_{\text{C}}$ from our methodology) of $\sim$ 4800.