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arXiv · 1311.5052

Robust estimation of risks from small samples

Simon H. Tindemans·Goran Strbac
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Abstract

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 nonparametric 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.

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Simon H. Tindemans, Goran Strbac. 2017-05-05. Robust estimation of risks from small samples. https://doi.org/10.1098/rsta.2016.0299

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