In this thesis, we develop and test a technology for computer-assisted assessments of newborn brain maturity from sleep electroencephalogram (EEG). Brain maturation of newborns is reflected in rapid development of EEG patterns over a number of weeks after conception. Observing the maturational patterns, experts can assess newborn’s EEG maturity with an accuracy ±2 weeks of newborn’s stated age. A mismatch between the EEG patterns and newborn’s physiological age alerts clinicians about possible neurological problems. Analysis of newborn EEG requires specialised skills to recognise the maturity-related waveforms and patterns and interpret them in the context of newborns age and behavioural state. It is highly desirable to make the results of maturity assessment most accurate and reliable. However, the expert analysis is limited in capability to estimate the uncertainty in assessments. To enable experts quantitatively evaluate risks of brain dysmaturity for each case, we employ the Bayesian model averaging methodology. This methodology, in theory, provides the most accurate assessments along with the estimates of uncertainty, enabling experts to take into account the full information about the risk of decision making. Such information is particularly important when assessing the EEG signals which are highly variable and corrupted by artefacts. The use of decision tree models within the Bayesian averaging enables interpreting the results as a set of rules and finding the EEG features which make the most important contribution to assessments. The developed technology was tested on approximately 1,000 EEG recordings of newborns aged 36 to 45 weeks post conception, and the accuracy of assessments was comparable to that achieved by EEG experts. In addition, it was shown that the Bayesian assessment can be used to quantitatively evaluate the risk of brain dysmaturity for each EEG recording.