Sensitivity of Bayes Inference with Data-Dependent Stopping Rules

It is sometimes argued that Bayesian inference is unaffected by data-dependent stopping rules.Although this can be true in a formal sense, it is likely that there will be heightened sensitivity to prior assumptions when data-dapendent rules are used rather than stopping rules that do not depend on the data.That is, there is an interaction between violations of prior assumptions and data-dependent stopping rules such that the violations have more severe consequences in repeated practice when data-dependent rules are used.We illustrate this fact in a simple example where 95% intervals are created using a flat prior when in fact the correct prior is normal with positive prior precision ..The coverage probabilities of the nominal 95% intervals are less tightly concentrated around .95 when data-dependent stopping rules are used, and the effect becomes stronger as . becomes larger.