Density of States and Bayesian Inference in Computational Mathematics

This lecture covers the computation of the density of states using nonequilibrium importance sampling, focusing on methods like thermodynamic integration and Wang Landau simulated tempering. It also delves into Bayesian inference, illustrating how to estimate evidence and posterior using importance sampling. The presentation extends to the application of these techniques in models like the Curie-Weiss model and a mixture of Gaussians, showcasing the challenges and advantages of the proposed estimators. The lecture concludes by highlighting the parallelizability and lower variance of the proposed method, emphasizing its effectiveness in complex estimation problems.