The current and future stability of the Antarctic ice sheet under rising global temperatures is critical to understand with wide-ranging implications, such as influencing ocean currents and having a significant contribution to global sea level rise. Sea level rise results in submergence of land as well as more regular and intense flooding, leading to wide-spread displacement of communities and collapse of coastal ecosystems. Climate models provide invaluable, spatiotemporally comprehensive estimates of past, current and future climatology that are integral for predictions of the stability of the Antarctic ice sheet - impact studies utilise the climate model product to predict events such as ice shelf collapse. Confidence in the findings of impact studies are partially limited though due to systematic errors in the climate model output that are difficult to quantify adequately across the ice sheet. The first aim of this thesis is to fill a gap in the literature by providing a thorough examination of systematic errors in state-of-the-art regional climate model simulations over Antarctica with a focus on: how the errors vary spatially across the ice sheet; the different sources of errors and their relative contributions; errors across different temporal scales; and errors in variables important for prediction of ice shelf collapse events, including snowfall, snow melt and near-surface air temperature. Following on from this, the second aim of the thesis is to develop a novel approach for bias correction that is specifically designed for the requirements of correcting climate model output over Antarctica. The bias correction methodology is developed with and tested against several simulated data examples and then subsequently with the real-world case study of correcting near-surface air temperature climate model output over the ice sheet using automatic weather station records. Throughout the thesis several statistical techniques are applied for the first time in this specific area of application, including techniques such as seasonal and trend decomposition using LOESS, Gaussian process regression and hierarchical Bayesian modelling. Utilising these techniques provides useful advantages over previous studies in the literature, including: presenting systematic errors at different temporal scales; explicitly modelling underlying spatial covariance patterns in the data and in systematic errors; and robustly estimating uncertainty in bias corrected climate model output.