The short satellite-observed period from 1979 to 2023 has seen the Antarctic sea ice changedramatically. The sea ice generally increased until 2014 then precipitously decreased from 2014 to 2017. Record lows were then observed in February 2022 and February 2023. To evaluate these recent changes in the context of anthropogenic climate change requires information on Antarctic sea ice variability over the full 20th century. However, only temporally and spatially sparse data are available before 1979, creating a need for statistical reconstructions. We create a stochastic ensemble reconstruction of monthly Antarctic sea ice extent from 1900-1979 using a novel Bayesian spatio-temporal model. This model produces a set of 2500 plausible reconstructions of sea ice extent by sector. These reconstructions improve on prior approaches with realistic month-to-month changes and interdecadal trends as well as plausible interactions between the sectors. These unique features allow the direct computation of extreme event probabilities for the pre-satellite period of the 20th century. For example, we compute a 0.44% probability of reconstructing a decline in total Antarctic sea ice extent as extreme or more extreme than the 2014-2017 decline. We compute a 16% probability of observing a sea ice minimum as low or lower than the February 2022 minimum in total sea ice extent of 2.22 mio. km2, and a probability of 4% for the February 2023 minimum of 2.04 mio. km2. We also propose a novel approach to modeling the Antarctic sea ice edge using a functional regression model. The sea ice edge on a given day is treated as a continuous set of points circling the South Pole and the latitudes of these points are modeled as a function of their longitude. This enables the estimation and visualization of a circumpolar annual cycle and interannual development of the sea ice, providing novel insight into the regionality of sea ice variability. We develop statistical techniques for reconstructing 1966-1978 Antarctic sea ice extent using early satellite images in the visible and infrared spectrum. These images have not previously been analyzed due to severe missingness and cloud cover occluding the sea ice. Combining extensive preprocessing with modern statistical methods, we produce monthly sea ice concentration maps from which we compute historic sea ice extent.