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Bayesian Model Mixing (BMM) is a statistical technique that can be used tocombine models that are predictive in different input domains into a compositedistribution that has improved predictive power over the entire input space. Weexplore the application of BMM to the mixing of two expansions of a function ofa coupling constant $g$ that are valid at small and large values of $g$respectively. This type of problem is quite common in nuclear physics, wherephysical properties are straightforwardly calculable in strong and weakinteraction limits or at low and high densities or momentum transfers, butdifficult to calculate in between. Interpolation between these limits is oftenaccomplished by a suitable interpolating function, e.g., Pad\'e approximants,but it is then unclear how to quantify the uncertainty of the interpolant. Weaddress this problem in the simple context of the partition function ofzero-dimensional $\phi^4$ theory, for which the (asymptotic) expansion at small$g$ and the (convergent) expansion at large $g$ are both known. We considerthree mixing methods: linear mixture BMM, localized bivariate BMM, andlocalized multivariate BMM with Gaussian processes. We find that employing aGaussian process in the intermediate region between the two predictive modelsleads to the best results of the three methods. The methods and validationstrategies we present here should be generalizable to other nuclear physicssettings.

Interpolating between small- and large-$g$ expansions using Bayesian Model Mixing