This paper reviews several statistical problems arising in Naval Engineering that the authors were involved with professionally or at NSWCCD over the past several years. The considered problems relate to statistical uncertainty, characterizing rare events, and ocean modeling, and naturally involve a stochastic component which needs to be accounted for through statistical methods. In statistical uncertainty, for example, one problem consists of constructing confidence intervals for measured quantities of interest (e.g. the variance of a ship motion) when temporal dependence in a signal needs to be taken into account. In characterizing rare events (e.g. ship capsizing or broaching to), a common problem is to estimate their frequency, which can be carried out under the umbrella of the statistical Extreme Value Theory. In ocean modeling, spatiotemporal statistical modeling of significant wave height has attracted much attention, especially in the context of modern treatments of “big data.” The focus throughout this work is on the theoretical underpinnings of these statistical problems, related work in the Statistics literature, and some open future directions.

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