  When collecting geocoded confidential data with the intent to disseminate,
agencies often resort to altering the geographies prior to making data publicly
available due to data privacy obligations. An alternative to releasing
aggregated and/or perturbed data is to release multiply-imputed synthetic data,
where sensitive values are replaced with draws from statistical models designed
to capture important distributional features in the collected data. One issue
that has received relatively little attention, however, is how to handle
spatially outlying observations in the collected data, as common spatial models
often have a tendency to overfit these observations. The goal of this work is
to bring this issue to the forefront and propose a solution, which we refer to
as "differential smoothing." After implementing our method on simulated data,
highlighting the effectiveness of our approach under various scenarios, we
illustrate the framework using data consisting of sale prices of homes in San
Francisco.
