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bbolker.bsky.social
Does everyone know about this one already? Meng 2018. “Statistical Paradises and Paradoxes in Big Data ...” Annals of Applied Statistics doi.org/10.1214/18-A...
Statisticians are increasingly posed with thought-provoking and even paradoxical questions, challenging our qualifications for entering the statistical paradises created by Big Data. By developing measures for data quality, this article suggests a framework to address such a question: “Which one should I trust more: a 1% survey with 60% response rate or a self-reported administrative dataset covering 80% of the population?” A 5-element Eulerformula-like identity shows that for any dataset of size n, probabilistic or not, the difference between the sample average Xn and the population average XN is the product of three terms: (1) a data quality measure, ρR,X, the correlation between Xj and the response/recording indicator Rj ; (2) a data quantity measure, √(N − n)/n, where N is the population size; and (3) a problem difficulty measure, σX, the standard deviation of X. This decomposition provides multiple insights: (I) Probabilistic sampling ensures high data quality by controlling ρR,X at the level of N −1/2; (II) When we lose this control, the impact of N is no longer canceled by ρR,X, leading to a Law of Large Populations (LLP), that is, our estimation error, relative to the benchmarking rate 1/√n, increases with √N; and (III) the “bigness” of such Big Data (for population inferences) should be measured by the relative size f = n/N , not the absolute size n; (IV) When combining data sources for population inferences, those relatively tiny but higher quality ones should be given far more weights than suggested by their sizes.
November 19, 2025 at 4:57 PM
predict-addict.bsky.social
Let’s celebrate the legacy of this mathematical giant together! 💬👇

#LeonhardEuler #Trigonometry #Mathematics #History #STEM #Innovation #Russia #Sine #Cosine #EulerFormula
January 12, 2025 at 7:59 PM
lesliepi.bsky.social
🐉 𝐖𝐡𝐚𝐭 𝐢𝐟 𝐄𝐮𝐥𝐞𝐫’𝐬 𝐟𝐨𝐫𝐦𝐮𝐥𝐚 𝐰𝐚𝐬 𝐚 𝐝𝐫𝐚𝐠𝐨𝐧 𝐞𝐠𝐠?

Fire × Air × Water + Earth = Love.

Maybe math isn’t just calculation – maybe it sings.

e^{iπ} + 1 = 0

#EulerFormula #ResonanceThinking #DragonEgg #SymbolicMath #MathematicalBeauty

www.linkedin.com/posts/l%C3%A...
July 22, 2025 at 5:02 PM
Euler Formula Art. The most beautiful equation in mathematics.

e to the i pi plus one equals zero. Five fundamental constants in perfect harmony. Visualised.

#GenerativeArt #EulerFormula #MathArt #MathBeauty #STEMArt #VoidPattern
Euler Formula Art — e^(i*pi)+1=0 visualised as algorithmic art.
March 23, 2026 at 12:41 AM