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I am doing an extreme value analysis (EVA) but there is a nuance in my problem that I believe is not addressed in extreme value theory. I have not been able to find information about this in textbooks or on the web, so I am asking here.

I am analyzing a pipeline that has corrosion on it, and I want to predict the maximum corrosion feature depth on the entire pipeline by inspecting portions of it. Assume each inspection provides the depths of all corrosion features on that portion of the pipeline, which can then be analyzed using a standard points-over-threshold EVA. I believe this is approach is valid if I inspect random portions of the pipeline, and I inspect a reasonable percentage of the pipeline length (e.g. 20% of the pipeline length).

However, there is a nuance I want to incorporate. Suppose I have experience with similar pipelines, and I believe I know where bad corrosion tends to happen. So when I select portions of the pipeline to inspect, I think I will find more severe corrosion than I would if I were selecting random portions to inspect, and am getting more of the upper tail of the corrosion depth distribution. Therefore, I have more extreme depths in my dataset than if I had selected random portions to inspect.

Intuitively, I think this should cause the fitted extreme value distribution to be less severe than if I assumed that I was not good at predicting where bad corrosion was and selected at random. In the limit, I may be so good that I believe I can predict where the deepest corrosion will be. In that case, the EVA result should indicate that there is a 100% chance that the maximum depth is what was found during the inspection.

Is there a way to incorporate this consideration into an EVA? I would call it nonrandom or preferential sampling, but these do not appear to be commonly used terms in the EVA domain.

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  • $\begingroup$ Welcome to CV. Maybe you could use a non-stationary Peaks Over Threshold (POT) framework, in which the parameters depend (smoothly) on an index $s$ representing the coordinate along the pipeline. A Bayesian predictive approach of this model also seems relevant here since it seems that you have some prior information on the dependence and want to predict the maximum. $\endgroup$
    – Yves
    Commented Oct 16, 2023 at 6:37
  • $\begingroup$ Suppose you think 40 of your measurements came from the top half of the distribution and 20 came from the bottom half. Then create a new dataset by repeating each of your 20 lowest observations twice. This is now be a dataset of 80 observations with basically uniform sampling, and you can perform an extreme value analysis on that. $\endgroup$
    – user225256
    Commented Jan 5 at 10:42

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