  Atmospheric models used for weather and climate prediction are traditionally
formulated in a deterministic manner. In other words, given a particular state
of the resolved scale variables, the most likely forcing from the sub-grid
scale processes is estimated and used to predict the evolution of the
large-scale flow. However, the lack of scale-separation in the atmosphere means
that this approach is a large source of error in forecasts. Over recent years,
an alternative paradigm has developed: the use of stochastic techniques to
characterise uncertainty in small-scale processes. These techniques are now
widely used across weather, sub-seasonal, seasonal, and climate timescales. In
parallel, recent years have also seen significant progress in replacing
parametrisation schemes using machine learning (ML). This has the potential to
both speed up and improve our numerical models. However, the focus to date has
largely been on deterministic approaches. In this position paper, we bring
together these two key developments, and discuss the potential for data-driven
approaches for stochastic parametrisation. We highlight early studies in this
area, and draw attention to the novel challenges that remain.
