Extreme value estimation using the likelihood-weighted method

This paper proposes a practical approach to extreme value estimation for small samples of observations with truncated values, or high measurement uncertainty, facilitating reasonable estimation of epistemic uncertainty. The approach, called the likelihood-weighted method (LWM), involves Bayesian inference incorporating group likelihood for the generalised Pareto or generalised extreme value distributions and near-uniform prior distributions for parameters. Group likelihood (as opposed to standard likelihood) provides a straightforward mechanism to incorporate measurement error in inference, and adopting flat priors simplifies computation. The method's statistical and computational efficiency are validated by numerical experiment for small samples of size at most 10. Ocean wave applications reveal shortcomings of competitor methods, and advantages of estimating epistemic uncertainty within a Bayesian framework in particular.