There has been widespread adoption of single body-worn sensors to objectively capture the physical activity of free-living individuals in large studies across the world. For research into metabolic diseases such as obesity and diabetes, it is useful to use this data to assess activity energy expenditure, which requires development of inference models. This thesis describes the derivation and evaluation of models to estimate activity energy expenditure from acceleration data collected at either wrist or thigh. Two fundamentally different approaches were pursued; one follows a traditional approach of regressing metrics of movement intensity against activity energy expenditure, and one uses neural networks to learn a more complex relationship directly from the raw data. The performance of these models was then evaluated by agreement with a gold standard measure of energy expenditure in free-living humans. The generalisability of these models was then investigated by validating them in a large African cohort. Finally, the differences between the two methodological approaches were explored using a dataset of everyday activities performed in a laboratory. The movement intensity models accurately and precisely estimated activity energy expenditure in free-living adults with small and non-significant mean biases at the population level, and the neural network models offered a relatively modest but consistent increase in performance over their movement intensity counterparts. All models appeared to overestimate activity energy expenditure in the African population, which suggests that population specificity is a possibility, and caution should therefore be used when making international comparisons. There were systematic differences between the two modelling approaches when examined by activity type, indicating that the neural networks may be implicitly recognising activities, which may facilitate activity classification in free-living in the future. This works enhances the utility of raw acceleration signals now being collected in several large studies worldwide, and highlights the need for population-specific validity evaluation.