  Ordinary differential equation (ODE) model whose regression curves are a set
of solution curves for some ODEs, poses a challenge in parameter estimation.
The challenge due to the frequent absence of analytic solutions and the
complicated likelihood surface, tends to be more severe especially for larger
models with many parameters and variables. Yang and Lee (2020) proposed
state-space model with variational Bayes (SSVB) for ODE, capable of fast and
stable estimation in somewhat large ODE models. The method has shown excellent
performance in parameter estimation but has a weakness of underestimation of
the posterior covariance, which originates from the mean-field variational
method. This paper proposes a way to overcome the weakness, by using the
Laplace approximation. In numerical experiments, the covariance modified by the
Laplace approximation showed a high degree of improvement when checked against
the covariances obtained by a standard Markov chain Monte Carlo method. With
the improved covariance estimation, the SSVB renders fairly accurate posterior
approximations.
