Searching the entirety of Kepler data : new exoplanets and occurrence rate estimates

First, I present the results of an independent search of all ~200,000 stars observed over the four-year Kepler mission for multiplanet systems, using a three-transit minimum detection criteria to search orbital periods up to hundreds of days. My search returned 17 planet candidates in addition to thousands of known Kepler Objects of Interest (KOIs), with a 98.8% recovery rate of already confirmed planets. I highlight the discovery of one candidate, KIC-7340288 b, that is both rocky (radius < 1.6 R⊕) and in the habitable zone (insolation between 0.25 and 2.2 times the Earth's insolation). Another candidate is an addition to the already known KOI-4509 system. I also present adaptive optics imaging follow-up for six of my new candidates, two of which reveal a line-of-sight stellar companion within 4". Using my planet catalogue, I then present exoplanet occurrence rates estimated with approximate Bayesian computation for planets with radii between 0.5 and 16 R⊕ and orbital periods between 0.78 and 400 days, orbiting FGK dwarf stars. I characterize the efficiency of planet recovery by both my search and vetting pipelines using injection/recovery tests, and account for both planet radius uncertainty and the estimated false positive rate due to transit-like noise signals in the data, unlike the majority of previous works. By analyzing my FGK occurrence rates as well as those computed after separating F-, G-, and K-type stars, I explore dependencies on stellar effective temperature, planet radius, and orbital period. I reveal new characteristics of the photoevaporation-driven "radius gap" between ~1.5 and 2 R⊕, indicating that the significant bimodal distribution previously revealed for P < 100 days only exists over a much narrower range of orbital periods, above which sub-Neptunes dominate and below which super-Earths dominate. Finally, I provide several estimates of the "eta-Earth" value --- the frequency of potentially habitable, rocky planets orbiting Sun-like stars. For planets with sizes 0.75 - 1.5 R⊕ orbiting in a conservatively defined habitable zone (0.99 - 1.70 AU) around G-type stars, my calculations place an upper limit (84.1th percentile) of < 0.18 planets per star.Science, Faculty ofPhysics and Astronomy, Department ofGraduat