  The oxide pyrochlore Bi$_2$Ti$_2$O$_6$O$^\prime$ is known to be associated
with large displacements of Bi and O$^\prime$ atoms from their ideal
crystallographic positions. Neutron total scattering, analyzed in both
reciprocal and real space, is employed here to understand the nature of these
displacements. Rietveld analysis and maximum entropy methods are used to
produce an average picture of the structural non-ideality. Local structure is
modeled via large-box reverse Monte Carlo simulations constrained
simultaneously by the Bragg profile and real-space pair distribution function.
Direct visualization and statistical analyses of these models show the precise
nature of the static Bi and O$^\prime$ displacements. Correlations between
neighboring Bi displacements are analyzed using coordinates from the large-box
simulations. The framework of continuous symmetry measures has been applied to
distributions of O$^\prime$Bi$_4$ tetrahedra to examine deviations from
ideality. Bi displacements from ideal positions appear correlated over local
length scales. The results are consistent with the idea that these nonmagnetic
lone-pair containing pyrochlore compounds can be regarded as highly
structurally frustrated systems.
