  Accurately predicting the onset of specific activities within defined
timeframes holds significant importance in several applied contexts. In
particular, accurate prediction of the number of future users that will be
exposed to an intervention is an important piece of information for
experimenters running online experiments (A/B tests). In this work, we propose
a novel approach to predict the number of users that will be active in a given
time period, as well as the temporal trajectory needed to attain a desired user
participation threshold. We model user activity using a Bayesian nonparametric
approach which allows us to capture the underlying heterogeneity in user
engagement. We derive closed-form expressions for the number of new users
expected in a given period, and a simple Monte Carlo algorithm targeting the
posterior distribution of the number of days needed to attain a desired number
of users; the latter is important for experimental planning. We illustrate the
performance of our approach via several experiments on synthetic and real world
data, in which we show that our novel method outperforms existing competitors.
