[FOM] 2 problems in the foundations of statistics

Alasdair Urquhart urquhart at cs.toronto.edu
Sat Jul 30 08:50:38 EDT 2005

There is an illuminating discussion of these questions
in I.J. Good's classic monograph "The Estimation
of Probabilities: An Essay on Modern Bayesian Methods."

The history of the problem, as summarized by Good,
is as follows.  Laplace proposed the uniform distribution
as a prior in 1774.  The actuary G.F. Hardy in 1889 
suggested that a more flexible family of prior distributions
is given by the beta form; Lidstone (also an actuary) 
made the same proposal in 1920.  Good's book has 
a very fine discussion of the problem, including 
mathematical aspects, and generalization to 
multinomial estimation, where the appropriate 
family is the family of Dirichlet distributions.

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