Assessing daily patterns using home activity sensors and within period changepoint detection

We consider the problem of ascertaining daily patterns using passive sensors to establish a baseline for elderly people living alone. The data are whether or not some movement, or human related activity, has occurred in the previous 15 min. We seek to segment the broad patterns within a day, for example, awake/sleep times or potentially more activity around meal‐times. To address this problem we use changepoint detection which can segment the day into more/less active times. Traditional changepoint detection methods are inappropriate for these data as they fail to utilize the periodic nature of the data. The traditional assumption of conditional independence of the segments also hampers estimation of the within segment parameters. A new within‐period changepoint detection scheme is proposed that instead assumes a circular perspective of the time axis. This permits the pooling of evidence of changepoint events from across multiple days. Inference is performed within the Bayesian framework by utilizing the reversible jump Markov chain Monte Carlo sampler to explore the variable dimension parameter space. Simulations demonstrate that the sampler achieves high accuracy in approximating the posterior while being able to detect small segments. Application to four individuals from our industrial collaborator provides insights to their daily patterns.