39,739 research outputs found
The Fermi's Bayes Theorem
It is curious to learn that Enrico Fermi knew how to base probabilistic
inference on Bayes theorem, and that some influential notes on statistics for
physicists stem from what the author calls elsewhere, but never in these notes,
{\it the Bayes Theorem of Fermi}. The fact is curious because the large
majority of living physicists, educated in the second half of last century -- a
kind of middle age in the statistical reasoning -- never heard of Bayes theorem
during their studies, though they have been constantly using an intuitive
reasoning quite Bayesian in spirit. This paper is based on recollections and
notes by Jay Orear and on Gauss' ``Theoria motus corporum coelestium'', being
the {\it Princeps mathematicorum} remembered by Orear as source of Fermi's
Bayesian reasoning.Comment: 4 pages, to appear in the Bulletin of the International Society of
Bayesian Analysis (ISBA). Related links and documents are available in
http://www.roma1.infn.it/~dagos/history
Bayesian Posteriors Without Bayes' Theorem
The classical Bayesian posterior arises naturally as the unique solution of
several different optimization problems, without the necessity of interpreting
data as conditional probabilities and then using Bayes' Theorem. For example,
the classical Bayesian posterior is the unique posterior that minimizes the
loss of Shannon information in combining the prior and the likelihood
distributions. These results, direct corollaries of recent results about
conflations of probability distributions, reinforce the use of Bayesian
posteriors, and may help partially reconcile some of the differences between
classical and Bayesian statistics.Comment: 6 pages, no figure
Bayes' theorem and quantum retrodiction
We derive on the basis of Bayes' theorem a simple but general expression for the retrodicted premeasurement state associated with the result of any measurement. The retrodictive density operator is the normalized probability operator measure element associated with the result. We examine applications to quantum optical cryptography and to the optical beam splitter
Statistical Scientist Meets a Philosopher of Science: A Conversation
philosophy of science, philosophy of statistics, decision theory, likelihood, subjective probability, Bayesianism, Bayes theorem, Fisher, Neyman and Pearson, Jeffreys, induction, frequentism, reliability, informativeness
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