Markov Models

Markov models represent sequences and decisions as states linked by probabilistic transitions, making them useful when uncertainty and temporal dependence matter. Hidden Markov models use forward-backward inference and Baum–Welch estimation for unseen states, while Markov decision processes support planning and reinforcement learning; continuous-time chains also underpin discrete diffusion models. Researchers study how to learn transition kernels from limited or dependent data, build useful state abstractions, and scale inference and planning to large systems, with applications ranging from language generation to robotics and molecular dynamics. A central tension is that simple Markov states enable efficient analysis, but real systems may require richer memory to capture non-stationarity, partial observability, or slow mixing.