A Study on Akaike’s Bayesian Information Criterion in Wave Estimation

A feasibility study of Bayesian wave estimation was carried out to investigate the relationship between the minimum Akaike’s Bayesian information criterion (ABIC) and the estimated wave parameters. The ship response functions, which were used for the Bayesian wave estimation together with the ship motion cross spectra, were simply modified and compared with the normal response functions in connection with the accuracy of estimated wave parameters. Moreover, the concept of the ABIC surfaces was introduced to investigate the optimum estimates from the stochastic viewpoint and the physical viewpoint. As the result, it was revealed that the minimum ABIC did not always provide the best estimates from the viewpoint of wave estimation and the simply modified response functions could reduce the estimating errors in some cases. The reasons were considered that the estimating error at the sharp peak of response amplitude operators was closely related to existence of the local minima of the ABIC surface and the simply modified response functions had some effects to make the ABIC surface smoother. It is pointed out as the conclusion of this report that any estimating errors of the ship response functions were not considered in the Bayesian modeling.