  The concept of depth represents methods to measure how deep an arbitrary
point is positioned in a dataset and can be seen as the opposite of
outlyingness. It has proved very useful and a wide range of methods have been
developed based on the concept.
  To address the well-known computational challenges associated with the depth
concept, we suggest to estimate Tukey depth contours using recently developed
incremental quantile estimators. The suggested algorithm can estimate depth
contours when the dataset in known in advance, but also recursively update and
even track Tukey depth contours for dynamically varying data stream
distributions. Tracking was demonstrated in a real-life data example where
changes in human activity was detected in real-time from accelerometer
observations.
