  The Bayes factor, the data-based updating factor of the prior to posterior
odds of two hypotheses, is a natural measure of statistical evidence for one
hypothesis over the other. We show how Bayes factors can also be used for
parameter estimation. The key idea is to consider the Bayes factor as a
function of the parameter value under the null hypothesis. This 'Bayes factor
function' is inverted to obtain point estimates ('maximum evidence estimates')
and interval estimates ('support intervals'), similar to how P-value functions
are inverted to obtain point estimates and confidence intervals. This provides
data analysts with a unified inference framework as Bayes factors (for any
tested parameter value), support intervals (at any level), and point estimates
can be easily read off from a plot of the Bayes factor function. This approach
shares similarities but is also distinct from conventional Bayesian and
frequentist approaches: It uses the Bayesian evidence calculus, but without
synthesizing data and prior, and it defines statistical evidence in terms of
(integrated) likelihood ratios, but also includes a natural way for dealing
with nuisance parameters. Applications to real-world examples illustrate how
our framework is of practical value for making quantitative inferences.
