Interpolating between small- and large-x expansions using Bayesian Model Mixing

Bayesian Model Mixing (BMM) is a statistical technique used to combine models that are valid in different input domains into a composite distribution that has good statistical properties over the entire input space. This is done by weighting each of the models being mixed so that each one contributes to the composite distribution in the regions of the input space where it is valid. In this talk I will present an application of BMM to the problem of mixing two expansions of a function: one that is valid at small values, and the other at large values, of a coupling constant. Interpolation between these limits is often accomplished by choice of a suitable interpolating function, e.g., Padé approximants, but uncertainty quantification (UQ) is difficult in such approaches. One example of such a problem is the partition function of zero-dimensional φ⁴ theory for which the (asymptotic) expansion at small g and the (convergent) expansion at large g are both known. I will show results from the application of BMM to this problem and discuss the UQ that results from employing BMM and statistical models for the accuracy of the series that describe the two limiting cases.