Laplace's theory of errors

Abstract

The genesis and development of the theory of errors before Laplace have been considered in a series of my articles [69] -[74]. My present aim is to elucidate the relevant work of Laplace himself, which hitherto I have considered only in connection with finite random sums [72] *. Laplace's contributions divide naturally into the Theorie analytique des probabilites (hereafter called TAP), first published in 1812 (and its supplements published in 1820), and the writings prior to this. These writings2 are studied in §§ 2-5, and the relevant places of the TAP in §§ 6-9; §§ 10 and 12-13 are devoted to somewhat specific subjects related to my theme, while §11 is an attempt to describe the limitations of Laplace's theory of errors. Several facts must be noted in following the text below. 1. Laplace's notation for f(x)dx = P{x^C^x + dx} is f(x) = P{C = x}. 2. Laplace's expression le veritable instant or, more generally, "the true value", is now part of the classical error theory. The different viewpoint of mathematical statistics employs the concept of parameters (specifically, location parameters) of distribution laws.