Individual and Statistical Characterization of the Giant Exoplanet Population

The field of observational exoplanet astronomy has seen tremendous progress over the span of only a few decades. Now, we find ourselves at the dawn of a new era: the characterization of distant worlds. Novel observational methods and statistical techniques allow us to explore not only the trends in bulk properties within the exoplanet population, but the atmospheric properties of individual planets as well. In this thesis, we aim to produce a more comprehensive view of the giant exoplanet population across a range of orbital distances, from the chemical inventory, thermal structure, and orbital characteristics of hot Jupiters, to the occurrence rate of cold giants and their correlation with inner planets. We begin by characterizing the orbital parameters of a single hot Jupiter, reporting on the spin-orbit misalignment and precession of the planetary system based on gravity-darkened transit observations. We then investigate the composition and thermal structure of an ultra hot Jupiter atmosphere, searching for water vapor and TiO in its optical transmission and emission spectra. We also provide confirmation of neutral atomic iron in the day-side atmosphere of an ultra hot Jupiter, and introduce a new likelihood mapping technique to constrain a planet's day-night contrast and peak phase offset using high-resolution Doppler spectroscopy alone for the first time. Lastly, we turn out attention to characterizing the population of outer planets. We perform an automated search for and statistical study of transiting cold giant planets orbiting Sun-like stars, discussing their occurrence rate, radius distribution, and correlation with inner planets. These works will have implications for theories of planet formation at both the inner and outer edges of planetary systems, allowing us to develop a clearer understanding of planet formation and evolution. The breadth of these studies is also a testament to the advancing capabilities of observational exoplanet science, and we anticipate that the future of the field lies in the study of Earth-like planets and the statistical trends in atmospheric properties across the exoplanet population.Ph.D