Julien Langou : July 30, 2009

Translation and modern interpretation of thirteen pages of Laplace's 1820 treatise

Julien Langou, University of Colorado, Denver

Thursday, July 30, 10:00 a.m. in the CERFACS conference room

Abstract:

In Sur l'application du calcul des probabilités à la philosophie naturelle, (Théorie Analytique des Probabilités. Troisième Edition. Premier Supplément), 1820, Laplace provides an important scientific contribution ranging from Statistic, Linear Algebra to Astronomy. We mainly provide an English translation of Laplace's manuscript (originally in French). We also add a few comments to put the manuscript in a current context.

In this manuscript, Laplace explains how to compute the variance of two variables of a linear statistical model. His algorithm can be interpreted as performing the Cholesky factorization of the normal equations and then compute the two variances from the Cholesky factor. A second method used by Laplace to justify the first is to perform a QR factorization of the regression matrix and compute the variance from the R factor. Laplace was performing the QR factorization through the modified Gram-Schmidt algorithm. Laplace also demonstrates how to use this algorithm on an astronomical example.

Laplace did not know what a factorization was, nor a matrix. We interpret his result through factorizations but certainly do not claim that Laplace invented all this.