146 Metastatistics for the Non-Bayesian Regression Runner
–.50.51Pre-treatment attribute: balance achieved0 .1.2.3.4.5.6.7.8.9 1
Share of vote for union–.50.51Pre-treatment attribute: balance not achieved0 .1.2.3.4.5.6.7.8.9 1
Share of vote for unionFigure 3.8 Evidence for or against “balance” in a regression discontinuity design
unionization on the myriad of outcomes they examine, such as wages, enterprise
solvency, productivity, and so on. Limitations of scope prevent elaborating in more
detail, but the study by DiNardo and Lee points to an important problem with any
“non-severe” test of a hypothesis – Bayesian or non-Bayesian. If one takes the results
from DiNardo and Lee seriously, it is hard to see how the problem could even be
addressedwith individual data – irrespective of whether Bayesian or non-Bayesian
statistics were employed.
3.8 Concluding remarks
What I have written has only scratched the surface of longstanding disagreements.
For any suggestion of dissent with any “Bayesian” views discussed in this chapter,
there exists volumes of counter-arguments. Likewise, the debates among those who
do not employ Bayesian methods are no less voluminous. I, myself, don’t have a
single “theory of inference” to which I adhere.
As I have sought, for reasons of clarity, to highlight thedifferencesbetween
Bayesian and non-Bayesian perspectives, I risk overstating them. It seems fit-
ting, therefore, to conclude by illustrating that one can often find “non-Bayesian
features” in Bayesian work and “Bayesian features” in non-Bayesian work.
3.8.1 Bayesian doesn’t have to mean “not severe”
The idea that only non-Bayesians look for “severe tests,” or “try to learn from
errors,” is not correct. One nice example comes from a recent careful study by Kline