By 2039, it is projected that one in four people will be aged 65 or over. It is important we look for new ways to help and care for an ageing population. This thesis introduces new methods for identifying changes in behaviour within households, using observations from passive sensors placed within the homes of older people. First, we propose a novel method for detecting subtle changes in sequences whilst taking into account the natural day-to-day variability and differing numbers of ‘trigger’ events per day. Next we introduce a model to predict the probability a sensor will trigger throughout the day for a household, whilst considering the prior data and other sensors within the home. Finally, we present a framework to identify changes in probabilistic cluster membership of households across time. We assess the performance for each of these methods on simulated data and data provided through our partnership with Howz.