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General criteria

The dependence of Bayesian inferences on initial probability is considered by opponents as the fatal flaw in the theory. But this criticism is less severe than one might think at first sight. In fact: It is well known to all experienced physicists that conclusions drawn from an experimental result (and sometimes even the ``result'' itself!) often depend on prejudices about the phenomenon under study. Some examples:
Figure: Results on two physical quantities as a function of the publication date.
\begin{figure}\centering\epsfig{file=dago24.eps,width=12.5cm,height=18cm,clip=}\end{figure}
These comments are not intended to justify unscrupulous behaviour or sloppy analysis. They are intended, instead, to remind us -- if need be -- that scientific research is ruled by subjectivity much more than outsiders imagine. The transition from subjectivity to ``objectivity'' begins when there is a large consensus among the most influential people about how to interpret the results3.11.
Figure: $ R=\sigma_L/\sigma_T$ as a function of the Deep Inelastic Scattering variable $ x$ as measured by experiments and as predicted by QCD.
\begin{figure}\centering\epsfig{file=rqcd3.eps,height=19cm,clip=}\end{figure}

In this context, the subjective approach to statistical inference at least teaches us that every assumption must be stated clearly and all available information which could influence conclusions must be weighed with the maximum attempt at objectivity3.12.

What are the rules for choosing the ``right'' initial probabilities? As one can imagine, this is an open and debated question among scientists and philosophers. My personal point of view is that one should avoid pedantic discussion of the matter, because the idea of universally true priors reminds me terribly of the famous ``angels' sex'' debates.

If I had to give recommendations, they would be the following.


next up previous contents
Next: Insufficient reason and maximum Up: Choice of the initial Previous: Choice of the initial   Contents
Giulio D'Agostini 2003-05-15