Does an Observed Sequence of Numbers Follow a Simple Rule? (Another Look at Bode's Law)

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Abstract
In a recent article I. J. Good has used Bayesian methods to conclude that there is strong evidence in favor of the validity of Bode's law. Here we reanalyze the observed planetary distances using non-Bayesian significance testing procedures, and reach the opposite conclusion. The three purposes of this article are (1) to reexamine the validity of Bode's law; (2) to develop some insight into the more general problem of testing whether or not an observed sequence of numbers follows some simple rule; and (3) to discuss the philosophical basis of Fisherian significance testing. It is not intended to provide an example of disagreement between Bayesian and non-Bayesian methods. Rather the two analyses are seen to be similar in execution, the different conclusions arising from different choices of the statistical models.

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