Ordered Matrix Dirichlet

The Ordered Matrix Dirichlet (OMD) is a probability distribution used to model ordered stochastic matrices, finding applications in various fields requiring the analysis of ordered categorical data and dynamic systems. Current research focuses on incorporating OMD priors into state-space models, particularly hidden Markov models, and employing it within neural network architectures for tasks like image fusion and preconditioning iterative solvers. This work is significant because it allows for the incorporation of prior knowledge about ordering into models, leading to improved interpretability and performance in diverse applications such as international relations modeling, gait recognition, and federated learning with heterogeneous data.