Kavli Affiliate: Jia Liu
| First 5 Authors: Shehzaib Irfan, Shehzaib Irfan, , ,
| Summary:
Extreme value theory (EVT) is well suited to model extreme events, such as
floods, heatwaves, or mechanical failures, which is required for reliability
assessment of systems across multiple domains for risk management and loss
prevention. The block maxima (BM) method, a particular approach within EVT,
starts by dividing the historical observations into blocks. Then the sample of
the maxima for each block can be shown, under some assumptions, to converge to
a known class of distributions, which can then be used for analysis. The
question of automatic (i.e., without explicit expert input) selection of the
block size remains an open challenge. This work proposes a novel Bayesian
framework, namely, multi-objective Bayesian optimization (MOBO-D*), to optimize
BM blocking for accurate modeling and prediction of extremes in EVT. MOBO-D*
formulates two objectives: goodness-of-fit of the distribution of extreme
events and the accurate prediction of extreme events to construct an estimated
Pareto front for optimal blocking choices. The efficacy of the proposed
framework is illustrated by applying it to a real-world case study from the
domain of additive manufacturing as well as a synthetic dataset. MOBO-D*
outperforms a number of benchmarks and can be naturally extended to
high-dimensional cases. The computational experiments show that it can be a
promising approach in applications that require repeated automated block size
selection, such as optimization or analysis of many datasets at once.
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