Data assimilation: A dynamic homotopy-based coupling approach

Homotopy approaches to Bayesian inference have found widespread use especially if the Kullback-Leibler divergence between the prior and the posterior distribution is large. Here we extend one of these homotopy approach to include an underlying stochastic diffusion process. The underlying mathematical problem is closely related to the Schr\"odinger bridge problem for given marginal distributions. We demonstrate that the proposed homotopy approach provides a computationally tractable approximation to the underlying bridge problem. In particular, our implementation builds upon the widely used ensemble Kalman filter methodology and extends it to Schr\"odinger bridge problems within the context of sequential data assimilation.