Variational State and Parameter Estimation
This work provides an incremental improvement for researchers and practitioners working with nonlinear state-space models by offering a deterministic and efficient approximation method.
This paper addresses the problem of computing Bayesian estimates for states and model parameters in nonlinear state-space models. It proposes a variational approach that approximates the intractable distribution, leading to an optimization problem with readily available first- and second-order derivatives for efficient solutions. The method is compared against Hamiltonian Monte Carlo in two numerical examples.
This paper considers the problem of computing Bayesian estimates of both states and model parameters for nonlinear state-space models. Generally, this problem does not have a tractable solution and approximations must be utilised. In this work, a variational approach is used to provide an assumed density which approximates the desired, intractable, distribution. The approach is deterministic and results in an optimisation problem of a standard form. Due to the parametrisation of the assumed density selected first- and second-order derivatives are readily available which allows for efficient solutions. The proposed method is compared against state-of-the-art Hamiltonian Monte Carlo in two numerical examples.