Sensitivity of Bayes Inference with Data-Dependent Stopping Rules

Abstract

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 ρ. 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 ρ becomes larger.

Key Words:

• Sensitivity
• Bayesian inference
• Stopping rules
• Ignorable rules
• Missing data