English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The text of Laplace, \textit{Sur l'application du calcul des probabilit\'es\`a la philosophie naturelle,} (Th\'eorie Analytique des Probabilit\'es.Troisi\`eme \'Edition. Premier Suppl\'ement), 1820, is quoted in the context ofthe Gram-Schmidt algorithm. We provide an English translation of Laplace'smanuscript (originally in French) and interpret the algorithms of Laplace in acontemporary context. The two algorithms given by Laplace computes the mean andthe variance of two components of the solution of a linear statistical model.The first algorithm can be interpreted as {\em reverse square-root-freemodified Gram-Schmidt by row} algorithm on the regression matrix. The secondalgorithm can be interpreted as the {\em reverse square-root-free Cholesky}algorithm.

Translation and modern interpretation of Laplace's Th\'eorie Analytique des Probabilit\'es, pages 505-512, 516-520