Scanning transmission electron microscopy can directly image the atomic structure of materials. To resolve this structure, the material must be aligned along a direction such that columns of atoms are projected onto the image. The local relationships between the intensities and distances of these projected atom columns can inform our understanding of structure–property relationships to ultimately further improve the materials. Measurement error in the atom column locations can, however, introduce bias into parameter estimates. Here, we create a spatial Bayesian hierarchical model that treats the locations as parameters to account for measurement error, and lower the computational burden by approximating the likelihood using a non-contiguous block design around the atom columns. We conduct a simulation study and analyze real data to compare our model to standard spatial and non-spatial models. The results show our method corrects the bias in the parameter of interest, drastically improving upon the standard models.
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