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Bayesian statistics are based on a different philosophical approach for proof of inference.The mathematical formula for Bayes's theorem is: [|] = [|] [] []The formula is read as the probability of the parameter (or hypothesis =h, as used in the notation on axioms) “given” the data (or empirical observation), where the horizontal bar refers to "given".
Proofs from THE BOOK is a book of mathematical proofs by Martin Aigner and Günter M. Ziegler. The book is dedicated to the mathematician Paul Erdős, who often referred to "The Book" in which God keeps the most elegant proof of each mathematical theorem. During a lecture in 1985, Erdős said, "You don't have to believe in God, but you should ...
Proofs That Really Count: the Art of Combinatorial Proof is an undergraduate-level mathematics book on combinatorial proofs of mathematical identies.That is, it concerns equations between two integer-valued formulas, shown to be equal either by showing that both sides of the equation count the same type of mathematical objects, or by finding a one-to-one correspondence between the different ...
The Politics of Large Numbers:A History of Statistical Reasoning is a book by French statistician, sociologist and historian of science, Alain Desrosières, which was originally published in French in 1993. [1] The English translation, by Camille Naish, was published in 1998 by Harvard University Press. [2]
In his book Statistics as Principled Argument, Robert P. Abelson presents the perspective that statistics serve as a standardized method for resolving disagreements among scientists, who could otherwise engage in endless debates about the merits of their respective positions. From this standpoint, statistics can be seen as a form of rhetoric.
Reissued as Statistical Methods Applied to Experiments in Agriculture and Biology in 1940 and then again as Statistical Methods with Cochran, WG in 1967. A classic text. Importance: Influence. Principles and Procedures of Statistics with Special Reference to the Biological Sciences. Authors: Steel, R.G.D, and Torrie, J. H.
Gauss brought the work of his predecessors together with his own original work into a systematic framework, filled in gaps, corrected unsound proofs, and extended the subject in numerous ways. The logical structure of the Disquisitiones (theorem statement followed by proof, followed by corollaries) set a standard for later texts. While ...
Bertrand's postulate and a proof; Estimation of covariance matrices; Fermat's little theorem and some proofs; Gödel's completeness theorem and its original proof; Mathematical induction and a proof; Proof that 0.999... equals 1; Proof that 22/7 exceeds π; Proof that e is irrational; Proof that π is irrational