In 1812, Laplace issued his Théorie analytique des probabilités in which he laid down
many fundamental results in statistics. The first half of this treatise was concerned with
probability methods and problems, the second half with statistical methods and applications.
Laplace’s proofs are not always rigorous according to the standards of a later day, and his
perspective slides back and forth between the Bayesian and non-Bayesian views with an ease that
makes some of his investigations difficult to follow, but his conclusions remain basically sound
even in those few situations where his analysis goes astray.
In 1819, he published a popular account of his work on probability. This book bears the same
relation to the Théorie des probabilités that the Système du monde does to the Méchanique céleste.
In its emphasis on the analytical importance of probabilistic problems, especially in the context of
the “approximation of formula functions of large numbers,” Laplace’s work goes beyond the
contemporary view which almost exclusively considered aspects of practical applicability.
Laplace’s Théorie analytique remained the most influential book of mathematical probability theory
to the end of the 19th century. The general relevance for statistics of Laplacian error theory was
appreciated only by the end of the 19th century. However, it influenced the further development of a
largely analytically oriented probability theory. (資料來源)