Joint Distributional Forecasting

Background: Probabilistic forecasting models for dynamical systems benefit from evolving predictive distributions directly rather than reconstructing them via ensemble sampling.

Question / Future Work: The current implementation models marginal predictive distributions for each state dimension rather than the full joint distribution over the complete state vector. A future extension is to develop the framework to operate directly on the full joint predictive distribution-to-distribution, which requires finding scalable parameterizations for high-dimensional dependence structures and covariance representations.