Accounting for Location Measurement Error in Imaging Data with Application to Atomic Resolution Images of Crystalline Materials

Abstract: Scientists use imaging to identify objects of interest and infer properties of these objects. The locations of these objects are often measured with error, which when ignored leads to biased parameter estimates and inflated variance. Current measurement error methods require an estimate or knowledge of the measurement error variance to correct these estimates, which may not be available. Instead, we create a spatial Bayesian hierarchical model that treats the locations as parameters, it using the image itself to incorporate positional uncertainty. We lower the computational burden by approximating the likelihood using a non-contiguous block design around the object locations. We apply this model in a materials science setting to study the relationship between the chemistry and displacement of hundreds of atom columns in crystal structures directly imaged via scanning transmission electron microscopy. Greater knowledge of this relationship can lead to engineering materials with improved properties of interest. We find strong evidence of a negative relationship between atom column displacement and the intensity of neighboring atom columns, which is related to the local chemistry. A simulation study shows our method corrects the bias in the parameter of interest and drastically improves coverage in high noise scenarios compared to non-measurement error models.