The accident risk of severe (≥5 fatalities) accidents in fossil energy chains (Coal, Oil and Natural Gas) is analyzed. The full chain risk is assessed for Organization for Economic Co-operation and Development (OECD), 28 Member States of the European Union (EU28) and non-OECD countries. Furthermore, for Coal, Chinese data are analysed separately for three different periods, i.e., 1994–1999, 2000–2008 and 2009–2016, due to different data sources, and highly incomplete data prior to 1994. A Bayesian Model Averaging (BMA) is applied to investigate the risk and associated uncertainties of a comprehensive accident data set from the Paul Scherrer Institute’s ENergy-related Severe Accident Database (ENSAD). By means of BMA, frequency and severity distributions were established, and a final posterior distribution including model uncertainty is constructed by a weighted combination of the different models. The proposed approach, by dealing with lack of data and lack of knowledge, allows for a general reduction of the uncertainty in the calculated risk indicators, which is beneficial for informed decision-making strategies under uncertainty.