I will present recent work on the construction of stochastic parameterizations by statistical inference from high-resolution model datasets. Large Eddy Simulation (LES) models are able to resolve atmospheric convection, but are too expensive to run on large domains. However, data from LES models on limited domains can be used to estimate stochastic processes that mimick the LES convective response to the large-scale atmospheric state. These stochastic processes are conditional on the large-scale state. They are formulated as discrete processes (conditional Markov chains), allowing for easy estimation and computation. The discrete states correspond to different convective states (turbulent flux states, or cloud types). I will discuss application of this approach to LES datasets for shallow and deep convection.