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August 11, 2008

Bayes' Theorem

A Useful Tool, But Easily Misused

Over two hundred years ago, the Reverend Thomas Bayes (1701(?)-1761) wrote a paper, later published posthumously, entitled "An essay towards solving a problem in the doctrine of chances," in which he developed a theorem for evaluating the probability of a conclusion's being true, which in turn depends upon other conditions that are themselves probabilistic in nature. It remained little noticed other than by statisticians until recent years, when it became something of a fad in various areas of science, one reason being availability of the requisite powerful computational techniques. Among other things, it is being used to address such questions as determining the reliability of rival theories and the confidence value that should be assigned to anomalous data that contradicts established ideas.

As with most powerful tools, it can be a valuable asset when properly used, but a source of mischief and damage when misapplied. Points that need to be taken into consideration include:

-- Bayes’ idea of calculating “the probability of getting observed results on the basis of each of the rival theories” can be useful in comparing situations that involve small variations on initial beliefs, but it misrepresents comparisons between conclusions arising from radically different assumptions. In particular, where a new paradigm challenges a prevailing belief system, the necessarily highly subjective assessment of the probabilities involved will always cause the theory based on familiar assumptions to calculate out as more credible than one introducing unfamiliar assumptions. Bayesian probabilities are little more than digitized familiarities.

-- Probability arguments are inappropriate when the question boils down to either accepting the validity of an observation or not.

-- Results become undependable when dealing with events that are comparatively rare

The whys are summarized clearly and simply by Professor Don Scott in a piece on his web site entitled "Statistics--Tool or Weapon?" at http://www.electric-cosmos.org/Bayes.pdf, in which he also explains why attempts to discredit Halton Arp's observations of quasar redshifts by such methods are misfounded. Wall Thornhill also discusses the subject in his posting "Whatever Happened to Real Science?" at http://www.holoscience.com/news.php?article¥7ya4dj

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