Inductive inference to a personal God via Bayes' Theorem presupposes a well-defined reference class of universes, which does not exist and renders prior probability assignments arbitrary.

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Bayes' Theorem(as used in probability and epistemology): A mathematical rule that shows how to update your beliefs when you get new evidence, named after Thomas Bayes, an 18th-century mathematician.
Prior probability(Used to argue that theism's low prior probability is not overcome by ambiguous or absent evidence): The intrinsic probability of a hypothesis before taking any evidence into account
Reference class(Boorse's biostatistical theory): A biologically relevant subgroup of a species used to specify the population mean against which individual functional efficiency is measured, accounting for the fact that not all members of a species share the same design in every respect
arbitrary(Debate over Locke's watch passage and natural kind classification): Does not mean 'random' or that all qualities are equally adequate as differentia; refers instead to the availability of multiple similarly good and natural grounds for classification.

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