  Bayesian Model Mixing (BMM) is a statistical technique that can be used to
combine models that are predictive in different input domains into a composite
distribution that has improved predictive power over the entire input space. We
explore the application of BMM to the mixing of two expansions of a function of
a coupling constant $g$ that are valid at small and large values of $g$
respectively. This type of problem is quite common in nuclear physics, where
physical properties are straightforwardly calculable in strong and weak
interaction limits or at low and high densities or momentum transfers, but
difficult to calculate in between. Interpolation between these limits is often
accomplished by a suitable interpolating function, e.g., Pad\'e approximants,
but it is then unclear how to quantify the uncertainty of the interpolant. We
address this problem in the simple context of the partition function of
zero-dimensional $\phi^4$ theory, for which the (asymptotic) expansion at small
$g$ and the (convergent) expansion at large $g$ are both known. We consider
three mixing methods: linear mixture BMM, localized bivariate BMM, and
localized multivariate BMM with Gaussian processes. We find that employing a
Gaussian process in the intermediate region between the two predictive models
leads to the best results of the three methods. The methods and validation
strategies we present here should be generalizable to other nuclear physics
settings.
