A Variational Approach to Path Estimation and Parameter Inference of Hidden Diffusion Processes

摘要

We consider a hidden Markov model, where the signal process,given by a diffusion, is only indirectly observed through somenoisy measurements. The article develops a variational methodfor approximating the hidden states of the signal process giventhe full set of observations. This, in particular, leads tosystematic approximations of the smoothing densities of thesignal process. The paper then demonstrates how an efficientinference scheme, based on this variational approach to theapproximation of the hidden states, can be designed to estimatethe unknown parameters of stochastic differential equations. Twoexamples at the end illustrate the efficacy and the accuracy ofthe presented method. color="gray">