Takami, TomokiTomokiTakamiKitahara, MasaruMasaruKitaharaMaki, AtsuoAtsuoMakiDostal, LeoLeoDostal2025-10-152025-10-152025-07-31ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering 11 (4): 04025060 (2025)https://hdl.handle.net/11420/58040This paper proposes a methodology to efficiently quantify an uncertainty in the probability density function (PDF) of excessive rolling of a ship. To this end, the Bayesian inference scheme is introduced to estimate the posterior distribution of roll damping terms, having measured instantaneous roll angles and incoming waves. This study employs two sampling techniques to estimate the posterior distribution: the transitional Markov chain Monte Carlo (TMCMC) and sequential and adaptive probabilistic integration (SAPI). Resulting posterior distributions of damping terms are compared and their computational tractability are discussed. Furthermore, analytical formulae are devised to predict an uncertainty zone in the PDF of roll angle embedding the damping terms up to the second order. By this means, the uncertainty in the PDF of excessive rolling can be quantitatively and efficiently evaluated, avoiding the so-called double loop problem. Numerical demonstrations are presented referring to synthetic roll motion measurements based on low- and high-fidelity 1 degree-of-freedom roll models; the latter incorporates higher-order damping terms.en2376-764220254ASCETechnology::600: TechnologyJournal Article10.1061/AJRUA6.RUENG-1626Journal Article