Title: Fine-Tuning in the Context of Bayesian Theory Testing,
Abstract: Fine-tuning in physics and cosmology is often used as evidence that a theory
is incomplete. For example, the parameters of the standard model of particle
physics are "unnaturally" small (in various technical senses), which has driven
much of the search for physics beyond the standard model. Of particular
interest is the fine-tuning of the universe for life, which suggests that our
universe's ability to create physical life forms is improbable and in need of
explanation, perhaps by a multiverse. This claim has been challenged on the
grounds that the relevant probability measure cannot be justified because it
cannot be normalized, and so small probabilities cannot be inferred. We show
how fine-tuning can be formulated within the context of Bayesian theory testing
(or \emph{model selection}) in the physical sciences. The normalizability
problem is seen to be a general problem for testing any theory with free
parameters, and not a unique problem for fine-tuning. Physical theories in fact
avoid such problems in one of two ways. Dimensional parameters are bounded by
the Planck scale, avoiding troublesome infinities, and we are not compelled to
assume that dimensionless parameters are distributed uniformly, which avoids
non-normalizability.