Tag: Probability Theory
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Interval Filters for Pre-Selection in Model-Assisted Constrained Pareto Optimization
Michael Emmerich, JYU, Finland, 28.1.2026 When objective and constraint evaluations are expensive (CFD/FEM, digital-twin simulations, etc.), we often rely on Gaussian process regression (Kriging) as a surrogate. A GP does not only predict a mean vector, it also delivers uncertainty. Interpreted component-wise, this uncertainty naturally forms an axis-aligned confidence box in for objectives (and similarly…
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The Gumbel Distribution, Extreme Rainfall, and the Euler–Mascheroni Constant
Nature doesn’t just have averages; it has extremes—the hottest day, the strongest wind, the largest daily rainfall, the highest flood. For extremes, a universal statistical law often appears: the Gumbel distribution. In this post, we meet it through a simple and realistic story about annual maximum rainfall, learn how a basic normalization makes its shape…
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Überlichtschnelle Quantenkommunikation? – Zwischen Einsteins Hypothese und Bells Experiment (in German)
In diesem Beitrag versuche ich, auf einfache Weise darzustellen, wie mithilfe der Wahrscheinlichkeitsrechnung in einem Experiment festgestellt werden kann, ob ein System verborgene Variablen besitzt. Diese Methode ist von herausragender Bedeutung, da sie den statistischen Nachweis erbringt, dass Quantenkommunikation quasi instantan – also schneller als Lichtgeschwindigkeit – ablaufen kann. Gleichzeitig werden zentrale Prinzipien der Quantenmechanik…
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Of Autumn Leaves and Coupon Collectors
Essay by Michael Emmerich, October 11th, 2024 Imagine a peaceful autumn day where leaves gently fall, covering a patch of land. The land can be represented as a grid or matrix with distinct places, each starting uncovered. As the leaves fall, they randomly land on one of these places, gradually covering the ground. But how…
Michael Emmerich 