Bayesian Inference for Functional Extreme Events with Partial Observations

This paper addresses the challenge of analyzing extreme events of a stochastic process when only partial observations are available. It proposes a Bayesian MCMC algorithm to infer the parameters of the limiting process, the r-Pareto process, which describes the extremal behavior. The two-step approach effectively handles the unobserved parts of the process, allowing for more realistic modeling of extreme events in scenarios with limited data. The paper's significance lies in its ability to provide a robust framework for extreme value analysis in practical applications where complete process observations are often unavailable.