Annals of Mathematical Sciences and Applications

Volume 5 (2020)

Number 2

A note on parametric Bayesian inference via gradient flows

Pages: 261 – 282



Yuan Gao (Department of Mathematics, Duke University, Durham, North Carolina, U.S.A.)

Jian-Guo Liu (Department of Mathematics and Department of Physics, Duke University, Durham, North Carolina, U.S.A.)


In this note, we summarize several recent developments for efficient sampling methods for parameters based on Bayesian inference. To reformulate those sampling methods, we use different formulations for gradient flows on the manifold in the parameter space, including strong form, weak form and De Giorgi type duality form. The gradient flow formulations will cover some applications in deep learning, ensemble Kalman filter for data assimilation, kinetic theory and Markov chain Monte Carlo.


parameter updating, KL-divergence, generalized gradient flow

Received 6 November 2019

Accepted 21 December 2019

Published 13 October 2020