Translation and modern interpretation of Laplace’s Théorie Analytique des Probabilités, pages 505-512, 516-520

نویسنده

  • Julien Langou
چکیده

The text of Laplace, Sur l’application du calcul des probabilités à la philosophie naturelle, (Théorie Analytique des Probabilités. Troisième Édition. Premier Supplément), 1820, is quoted in the context of the Gram-Schmidt algorithm. We provide an English translation of Laplace’s manuscript (originally in French) and interpret the algorithms of Laplace in a contemporary context. The two algorithms given by Laplace computes the mean and the variance of two components of the solution of a linear statistical model. The first algorithm can be interpreted as reverse square-root-free modified Gram-Schmidt by row algorithm on the regression matrix. The second algorithm can be interpreted as the reverse square-rootfree Cholesky algorithm.

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تاریخ انتشار 2009