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)
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