Passive monitoring in daily life may provide valuable insights into a person's health throughout the day. Wearable sensor devices play a key role in enabling such monitoring in a non-obtrusive fashion. However, sensor data collected in daily life reflect multiple health and behavior-related factors together. This creates the need for a structured principled analysis to produce reliable and interpretable predictions that can be used to support clinical diagnosis and treatment. In this work we develop a principled modelling approach for free-living gait (walking) analysis. Gait is a promising target for non-obtrusive monitoring because it is common and indicative of many different movement disorders such as Parkinson's disease (PD), yet its analysis has largely been limited to experimentally controlled lab settings. To locate and characterize stationary gait segments in free-living using accelerometers, we present an unsupervised probabilistic framework designed to segment signals into differing gait and non-gait patterns. We evaluate the approach using a new video-referenced dataset including 25 PD patients with motor fluctuations and 25 age-matched controls, performing unscripted daily living activities in and around their own houses. Using this dataset, we demonstrate the framework's ability to detect gait and predict medication induced fluctuations in PD patients based on free-living gait. We show that our approach is robust to varying sensor locations, including the wrist, ankle, trouser pocket and lower back.