(sec:ModelMixing)=
# Model averaging and mixing

In this chapter we discuss the challenge of combining the insights from a number of individual physics models to produce inference endowed with the physics models' collective wisdom. Section {ref}`sec:theory` provides the general setup for this problem, and introduces the crucial distinction between ${\cal M}$-closed and ${\cal M}$-open settings. Section {ref}`sec:BMA` describes the standard Bayesian solution: Bayesian Model Averaging (BMA); we then explain why BMA can only resolve the challenge in the ${\cal M}$-closed context. Section {ref}`sec:BMMgeneralities` then articulates paths to generalize BMA to a more sophisticated Bayesian Model Mixing (BMM), wherein we combine information from different models in a more textured way than BMA accomplishes. We end with Section {ref}`sec:stat_example`, which gives an example where BMM improves upon BMA by leveraging information on the local performance of two different models across the input domain.