Uncertainty quantification for model parameters and hidden state variables in Bayesian dynamic linear models

The quantification of uncertainty associated with the model parameters and the hidden state variables is a key missing aspect for the existing Bayesian dynamic linear models. This paper proposes two methods for carrying out the uncertainty quantification task: (a) the maximum a posteriori with the Laplace approximation procedure (LAP-P) and (b) the Hamiltonian Monte Carlo procedure (HMC-P). A comparative study of LAP-P with HMC-P is conducted on simulated data as well as real data collected on a dam in Canada. The results show that the LAP-P is capable to provide a reasonable estimation without requiring a high computation cost, yet it is prone to be trapped in local maxima. The HMC-P yields a more reliable estimation than LAP-P, but it is computationally demanding. The estimation results obtained from both LAP-P and HMC-P tend to the same values as the size of the training data increases. Therefore, a deployment of both LAP-P and HMC-P is suggested for ensuring an efficient and reliable estimation. LAP-P should first be employed for the model development and HMC-P should then be used to verify the estimation obtained using LAP-P.