Advancing Retrievals of Exoplanetary Spectra in the Era of Large Space-Based Telescopes

Exoplanet atmospheres tell the story of diverse worlds: what they are made of and how they came to be. We use theoretical models to make sense of the narrative encoded in each atmospheric data set. In particular, we extract information with retrievals, which couple statistical tools with high signal-to-noise spectral data to derive and estimate atmospheric properties. The inferred atmospheric structure and molecular abundances then influence our understanding of the Solar System in the context of exoplanets. Retrievals have become an essential tool in both understanding existing data and quantitatively informing the needs of future missions. Consequently, this thesis focuses on the interplay between data and models, the core components of a retrieval. First, I demonstrate the need to evaluate model assumptions in order to extract meaningful constraints from spectra. While varying in sophistication, most model-spectra comparisons fundamentally assume ``1D'' model physics. However, we know that planetary atmospheres are inherently ``3D'' in their structure and composition. Within a Bayesian retrieval framework, I show how the assumption of a single 1D thermal profile can bias our interpretation of the thermal emission spectrum of an unresolved hot Jupiter's atmosphere that is composed of two thermal profiles. I extend the application to full spectroscopic phase curves. For modern data, I reveal that the constraint for water vapor abundance is robust independent of model setup; however, methane is artificially well-constrained to incorrect values. Furthermore, I find that the 1D setup is insufficient at fitting data that the James Webb Space Telescope may measure, causing many abundance biases. Next, I develop an inverse modeling framework to estimate the science return of proposed missions that aim to perform reflected light spectroscopy of rocky exoplanets around Sun-like stars. By combining an albedo model, an instrument noise model, and a Bayesian inference tool, I explore retrievals of atmospheric and bulk properties as a function of data signal-to-noise ratio (SNR) and resolution (R). I present the recommended R and SNR combinations to achieve detection or constraint of key indicators of habitability on rocky planets such as water vapor, oxygen, and ozone