Exact Posterior

Exact posterior distributions, representing the updated beliefs about model parameters given observed data, are crucial for Bayesian inference but often computationally intractable. Current research focuses on developing efficient algorithms, such as Markov Chain Monte Carlo methods and improved variational inference techniques (including those using normalizing flows and Bernstein polynomials), to approximate or, in some specific cases, derive exact posteriors for complex models like Gaussian processes and switching dynamical systems. These advancements enable more accurate uncertainty quantification and improved inference in diverse applications, ranging from network analysis and time-series modeling to control systems and machine learning. The ability to obtain accurate posterior distributions directly impacts the reliability and interpretability of Bayesian models across various scientific disciplines.