Title: Searching for new discoveries in binary black hole mergers and of multi-messenger detections with gravitational-waves
Description: According to general relativity, appropriately accelerated masses emit gravitational radiation. With the gravitational-wave detectors reaching sufficient sensitivities for detecting astrophysical gravitational-waves, a new messenger for observing the astrophysical events has become available. However, with the current number of gravitational-wave detections, there are many unanswered questions whose answers are waiting to be discovered. Analogous to the Malmquist bias in other astronomical observation techniques, gravitational-wave detections also have an observation bias. In order to infer astrophysical distribution of the properties of gravitational-wave events from detections, this bias needs to be well understood. In this collection of studies, by investigating statistical and physical properties of gravitational-wave detection, an efficient semi-analytical method for calculating the bias was found. Further, the estimated bias was used for doing the first unmodelled inference on the mass distribution of binary black holes which showed additional structures not found by modelled inferences.

Vast majority of gravitational-wave detections are binary black hole mergers. One of the mysteries of binary black holes is their formation channels. There are several proposed formation scenarios none of which is strongly favored by data. One of these channels is the so-called hierarchical triple mergers which is an dynamical formation scenario expected to have in dense environments such as globular clusters. This scenario considers a bound three black hole system which gives two consecutive mergers. In this collection of studies, it was directly tested with the detections from the three observing runs of Advanced LIGO and Advanced Virgo detectors. No significant evidence for this scenario was found, individually interesting event pairs were identified for further investigation and upper limits on the occurrence of the scenario were obtained. Gravitational-wave detectors have sensitivity on the significant portion of the sky. However, the localizations of the gravitational-wave detections are not very precise.

Multi-messenger follow-ups guided by gravitational-wave detections can precisely locate the astrophysical source and gather more information by probing it with different messengers. The multi-messenger searches are done with statistical methods and it is necessary to have powerful statistical methods not to miss the valuable multi-messenger events. In the final parts of this collection of studies, optimal statistical methods for multi-messenger searches were developed and joint gravitational-wave and high-energy neutrino events were searched, both in realtime and with archival data.