The mathematics of uncertainty and randomness (probability) and of drawing sound conclusions from data (statistics). Probability theory traces to Pascal and Fermat's 1654 correspondence over a gambling dispute and was placed on a rigorous measure-theoretic footing by Andrey Kolmogorov in 1933; statistics developed largely independently, through Gauss's method of least squares and the hypothesis-testing framework built by Ronald Fisher, Jerzy Neyman and Egon Pearson in the early twentieth century.
Facts
Central QuestionHow can uncertainty, randomness and incomplete information themselves be reasoned about with mathematical precision, and what can data honestly be said to support? 1 Key DebateThe Bayesian versus frequentist divide over what a probability actually means, a rational agent's degree of belief, updated by evidence, against a long-run frequency of outcomes in repeated trials, a disagreement over a century old that still shapes how modern statistical inference is taught and practiced. 1 Cross-Tradition Connections
Associated With
Game theory shares its expected-value and optimization machinery with probability and statistics; mixed strategies are themselves probability distributions over pure strategies.
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