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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