THE THEORY OF PROBABILITIES.

By A. E. Bostwick. 1896

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A Kernel Test for Three-Variable Interactions (2013, background): “uniform on {−1, 1}, then (X,Y,XY ) is a pairwise independent but mutually dependent triplet [9].”
Quantum Mechanics as a Theory of Probability (2005, background): “ 6The inequalities were derived in [34]. The suﬃciency of the inequalities is due to Fine [35]. The polyhedral structure, its relation to logic, and its generalizations are discussed in [22, 36]. 7In [37], see also [8]. The parody of Kant is intended, I think. In his classic The Laws of Thought Bool”
Theory of classification : a survey of some recent advances (2005, background): “Inequality (12) is known as Hoeffding’s inequality [109], while (13) is referred to as Bernstein’s inequality [34].”
Concentration Inequalities (2008, background): “Moreover, for every t > 0, ¡ [Z ≥ Z + t] ≤ exp − Zh t Z and for every 0 t ≤ Z, ¡ [Z ≤ Z − t] ≤ exp − Zh − t Z By recalling that h(u) ≥ u 2 /(2 + 2u/3) for u ≥ 0 (we have already used this in the proof of Bernstein's inequality) and observing that h(u) ≥ u 2 /2 for u ≤ 0, we obtain the following im”
Prediction, learning, and games (2006, background): “The next inequality is a version of Bernstein’s inequality [25]; see also Freedman [110], Neveu [224].”
Mathematical Methods for Supervised Learning (2005, background): “…set K ⊂ B, approximation theory determines the best exponent r = r(K) > 0 3 for which dist(K,Sn)B ≤ CKn−r, n = 1, 2, . . . . (1.11) Such results are known in all classical settings in which B is one of the Lp spaces (with respect to Lebesgue measure) and K is given by a smoothness condition.”
Efficient Mechanisms for Peer Grading and Dueling Bandits (2018, background): “Therefore, we turn to the following tail bound, known as Bernstein’s inequality (Bernstein, 1946).”
A Tricentenary history of the Law of Large Numbers (2013, background): “De Morgan’s chief work on probability was, consequently, a lengthy article in the Encyclopedia Metropolitana usually cited as of 1845, but published as separatum in 1837 (De Morgan (1837)).”
Adaptive computation and machine learning (1998, background): “Although there exist many excellent textbooks on learning algorithms (see Duda and Hart (1973), Bishop (1995), Vapnik (1995), Mitchell (1997) and Cristianini and Shawe-Taylor (2000)) and on learning theory (see Vapnik (1982), Kearns and Vazirani (1994), Wolpert (1995), Vidyasagar (1997) and Anthony ”
Distribution-Free, Risk-Controlling Prediction Sets (2021, background): “The most well-known concentration result incorporating the variance is Bernstein’s inequality [38].”
Geometry of Quantum States: Index (2007, background): “(a) Bernstein [126] revealed that there exist cases in which three variables X, Y , Z are pairwise independent but not independent.”