|Outdoor sound propagation presents many computational challenges, including refraction by wind and temperature, interactions with heterogenous ground, complex surfaces such as buildings, and random scattering by turbulence. Given these challenges, it is important to characterize the uncertainties arising from imprecise knowledge of the atmosphere and terrain properties, and from random processes such as turbulence. Thus, it is natural to view outdoor sound propagation as stochastic prediction problem, much like forecasting the weather. This presentation describes a number of computational approaches and analyses inspired by this stochastic viewpoint. As a starting point, Monte Carlo simulations are considered, based on randomized realizations of the environment combined with physics-based propagation modeling using a parabolic equation. The resulting ensembles of propagation predictions can be used train surrogate models such as neural networks, or to evaluate explicit, physics-based models for the random signal distributions. With regard to the latter approach, newly derived, explicit forms for the distributions, based on extending the gamma distribution, are shown to be analytically convenient and provide excellent agreement with simulations. Furthermore, Bayesian methods based on these analytical distributions can be devised for applications such as signal classification and localization, and are shown to provide better performance than machine learning for an example dataset involving military ground vehicle classification.