The Biggest Vault: Crystallography’s Hidden Mathematical Codex
Bayes’ Theorem: Updating Beliefs in Crystallographic Inference
In crystallography, inference often evolves through conditional probability. Bayes’ Theorem transforms prior knowledge—such as expected atomic displacements or structural motifs—into refined posterior estimates from noisy diffraction data. For instance, when identifying phases in complex materials like high-temperature superconductors, the posterior P(A|B) combines known symmetry constraints with observed peak intensities. This iterative updating resolves ambiguities in defect modeling and disorder, enabling accurate electron density maps critical for understanding material behavior.