Fast Radio Burst Statistics in Space and Time

In this thesis I describe three statistical studies of fast radio bursts (FRBs), focusing on constraining the Milky Way’s (MW's) ionized halo, developing new spatial point process methodology for the identification of repeating FRBs, and performing (and maximizing the utility of) multi-wavelength observations of a nearby, active FRB. My FRB sample mainly comes from the revolutionary dataset from the FRB project of the Canadian Hydrogen Intensity Mapping Experiment (CHIME/FRB). The first project places upper limits on the total Galactic electron column as a function of Galactic latitude using FRB dispersion measures (DMs). By applying four different boundary models, I set observation-based constraints of the total Galactic DM contribution for $|b|\geq30^\circ$, depending on the Galactic latitude and selected model, that span 87.8$\,-\,141$\,pc\,cm$^{-3}$. These results suggest that some commonly used MW halo models overestimate the halo’s gas density, especially when assuming high halo masses. This work highlights the impact of feedback mechanisms in shaping the halo. The second project introduces a novel approach to inference on noisy nonhomogeneous Poisson processes (NHPPs), in particular describing the $k$-contact distribution for events in a noisy NHPP. Using a hierarchical Bayesian model, I first estimate hyperparameters that govern the intensity of the NHPP that describes CHIME/FRB's detection of independent FRBs on the sky. I then leverage the posterior distribution to infer the probability of detecting a given number of events within a certain radius in observation space. This approach has significantly increased sensitivity for identifying repeating FRB sources, increasing detection significance in 86\% of cases and decreasing the computed probability, the `probability of chance coincidence', by a median factor of around 3000 compared to the previous methodology. The third project focuses on searching for high-energy emission associated with an FRB, using contemporaneous X-ray and radio observations of the hyperactive and nearby repeating FRB source FRB 20220912A. Utilizing data from \xmm, \nicer, Effelsberg, CHIME/Pulsar, and CHIME/FRB, I place stringent upper limits on the X-ray to radio fluence ratio ($\eta_{\text{\,x/r}}$) at the time of radio bursts from the source. Despite detecting 30 radio bursts during the simultaneous X-ray observations, no significant X-ray emission was observed. Using a new Bayesian methodology that I developed, I set a 99.7\% credible interval upper limit on $\ate$ of $<2\times10^6$, the most stringent such limit for any FRB to date. These limits approach the level expected from proposed FRB emission mechanisms and observed phenomena from Galactic magnetars, especially when adopting an X-ray spectrum similar to that observed from the Galactic magnetar SGR 1935+2154 during its FRB-like emission. This thesis contributes to the field of FRB science by improving our understanding of the Milky Way’s halo and hence its co-evolution with the Galaxy and intergalactic medium, by developing novel statistical tools for identifying repeating FRBs and associations between other poorly-localized phenomena, and by placing deep limits on any associated X-ray emission of these enigmatic sources.

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