Abstract: Clouds and moist convection in the tropics are among the largest sources of uncertainties in state-of-the-art earth system models (ESMs) used for longtime weather predictions and climate change projections. The difficulty arrises from the fact that these models are based on a discretization of the equations of motion using grid mesh sizes ranging between 10km to 200km in the horizontal. These grids are too coarse to resolve clouds and moist dynamics in the tropics, and the associated dynamical and thermodynamical processes such as convective flows and latent heat exchange with the environment due to the phase change of water substances. As in many applications involving turbulent and multi-scale flows, the unresolved scale processes, or rather their effect on the resolved scales, are handled by sub-grid scale models often called parameterizations. The state-of-the-art parameterizations of clouds and moist convection in the tropics are based on a theory of large ensembles, known as the quasi-equilibrium (QE) theory, which fails dramatically to capture the most apparent modes of climate and weather variability in the tropics that operate on scales of thousands and tens of thousands kilometres such as the celebrated Madden and Julian oscillation (MJO) and monsoon intra-seasonal oscillations with periods of 40 days to 100 days. Contrarily to the QE assumption that requires some sort of scale separation between the resolved and the parameterized scales, convection in the tropics is organized on a hierarchy of scales ranging from the cloud cell of 1km to 10km to planetary scale disturbances such the MJO and monsoon oscillations. The dynamical and thermodynamical interactions across this vast range of temporal and spacial scales involves multi-scale tropical convective systems known as convectively coupled waves that are embedded in and interact with each other. The QE approximation tacitly makes the unresolved processes dynamically slaved to the resolved waves and thus unable to capture or represent the small scale fluctuations and their impact on the large scale waves. To overcome this dilemma, we use the framework of stochastic interacting particle systems to build stochastic birth and death models for multiple cloud types that are known to dominate organized tropical convection. Bayesian—machine learning-like—inference techniques are used in tandem to learn some key parameters of the cloud-cloud interactions, namely the associated transition time scales from one cloud type to another, based on radar data. The resulting, so-called, stochastic multi-cloud models have been successfully tested and implemented in research and operational ESMs and important improvements in the simulation of both the mean climatology and the large-scale tropical modes of variability such as the MJO monsoons have been established.