Extreme Risk & Dependence

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Abstractions about extreme values, heavy-tailed multivariate distributions, tail dependence, entropy-based thermodynamics, and uncertainty in scaling effects.

5 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Extreme value theory — A branch of statistics modeling the limiting behavior and tail risk of unusually large or small observations, especially block maxima and threshold exceedances.
• Maximum entropy thermodynamics — An inference-centered formulation of equilibrium thermodynamics that selects the probability distribution of greatest entropy subject to known macroscopic constraints.
• Multiplier Uncertainty — Represent uncertainty about how strongly a policy instrument changes its target, making optimal intervention depend on the distribution and covariance of the transmission coefficient rather than only its estimated mean.
• Multivariate Pareto distribution — A family of joint heavy-tailed distributions whose margins have Pareto-type behavior and whose dependence construction models simultaneous extremes across variables.
• Tail dependence — Measure whether two continuously distributed variables continue to co-exceed matched extreme quantiles by taking an upper- or lower-tail conditional-probability limit determined by their copula rather than their marginal scales.