  Hierarchical time series are common in several applied fields. The forecasts
for these time series are required to be coherent, that is, to satisfy the
constraints given by the hierarchy. The most popular technique to enforce
coherence is called reconciliation, which adjusts the base forecasts computed
for each time series. However, recent works on probabilistic reconciliation
present several limitations. In this paper, we propose a new approach based on
conditioning to reconcile any type of forecast distribution. We then introduce
a new algorithm, called Bottom-Up Importance Sampling, to efficiently sample
from the reconciled distribution. It can be used for any base forecast
distribution: discrete, continuous, or in the form of samples, providing a
major speedup compared to the current methods. Experiments on several temporal
hierarchies show a significant improvement over base probabilistic forecasts.
