Robust estimation of risks from small samples

Simon H. Tindemans*, Goran Strbac

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)


Data-driven risk analysis involves the inference of probability distributions from measured or simulated data. In the case of a highly reliable system, such as the electricity grid, the amount of relevant data is often exceedingly limited, but the impact of estimation errors may be very large. This paper presents a robust non-parametric Bayesian method to infer possible underlying distributions. The method obtains rigorous error bounds even for small samples taken from ill-behaved distributions. The approach taken has a natural interpretation in terms of the intervals between ordered observations, where allocation of probability mass across intervals is well specified, but the location of that mass within each interval is unconstrained. This formulation gives rise to a straightforward computational resampling method: Bayesian interval sampling. In a comparison with common alternative approaches, it is shown to satisfy strict error bounds even for ill-behaved distributions. This article is part of the themed issue 'Energy management: flexibility, risk and optimization'.

Original languageEnglish
Article number20160299
Pages (from-to)1-13
Number of pages13
JournalRoyal Society of London. Philosophical Transactions A. Mathematical, Physical and Engineering Sciences
Issue number2100
Publication statusPublished - 13 Aug 2017
Externally publishedYes


  • Bayesian inference
  • Dirichlet process
  • Imprecise probabilities
  • Non-parametric methods
  • Rare event analysis
  • Resampling methods


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