P-23

Two formulae of the marginal likelihood for parameter estimation using the ensemble Kalman filter

S. Nakano (The Institute of Statistical Mathematics)

In the framework of the state space modeling, unknown model parameters can be estimated on the basis of their marginal likelihood. In computing the marginal likelihood using the ensemble Kalman filter, we can consider two kinds of approximations. One is the Monte Carlo approximation in which the integral for obtaining the marginal likelihood is approximated by Monte Carlo integral. The other is the Gaussian approximation in which the integral is approximated based on a Gaussian approximation. These two formulae do not agree with each other even in linear Gaussian problems, and they provide different values in general. In this study, the performance of the parameter estimation based on the marginal likelihood was compared between these two formulae. It was confirmed that both formulae yield some Monte Carlo errors. In the case of linear Gaussian cases, the Monte Carlo approximation tended to provide worse marginal likelihood values. In addition, the estimate obtained by the Monte Carlo approximation was likely to be sometimes biased.