  The physics of ferroelectric domain walls is explored using the Bayesian
inference analysis of atomically resolved STEM data. We demonstrate that domain
wall profile shapes are ultimately sensitive to the nature of the order
parameter in the material, including the functional form of
Ginzburg-Landau-Devonshire expansion, and numerical value of the corresponding
parameters. The preexisting materials knowledge naturally folds in the Bayesian
framework in the form of prior distributions, with the different order
parameters forming competing (or hierarchical) models. Here, we explore the
physics of the ferroelectric domain walls in BiFeO3 using this method, and
derive the posterior estimates of relevant parameters. More generally, this
inference approach both allows learning materials physics from experimental
data with associated uncertainty quantification, and establishing guidelines
for instrumental development answering questions on what resolution and
information limits are necessary for reliable observation of specific physical
mechanisms of interest.
