Watson and Holmes propose ways of investigating robustness of statistical decisions by examining certain neighbourhoods around a posterior distribution. This may partly amount to ad hoc modelling of extra uncertainty.
Instead of creating neighbourhoods around the posterior a posteriori, we argue that it might be more fruitful to model a layer of extra uncertainty first, in the model building process, and then allow the data to determine how big the resulting neighbourhoods ought to be. We develop and briefly illustrate a general strategy along such lines.
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