Deep polar ice cores contain records of both past climate and trapped air that reflects past atmospheric compositions, notably of greenhouse gases. This record allows us to investigate the role of greenhouse gases in climate variations over eight glacial-interglacial cycles. The ice core record, like all paleoclimate records, contains uncertainties associated both with the relationships between proxies and climate variables, and with the chronologies of the records contained in the ice and trapped air bubbles. In this thesis, we develop a framework, based on Bayesian inverse modeling and the evaluation of complex probability densities, to accurately treat uncertainty in the ice core paleoclimate record. Using this framework, we develop two ...