Bayesian: probability of fire given current air data
Frequentist smoke alarm designed as most research is done:
Set the alarm trigger so as to have a 0.8 chance of detecting an inferno
Advantage of actionable evidence quantification:
Set the alarm to trigger when the posterior probability of a fire exceeds 0.02 while at home and at 0.01 while away
- Teaching clinical trialists to embrace Bayes when they already do in spirit but not operationally. Unlearning things is much more difficult than learning things.
- How to work with sponsors, regulators, and NIH principal investigators to specify the (usually skeptical) prior up front, and to specify the amount of applicability assumed for previous data.
- What is a Bayesian version of the multiple degree of freedom "chunk test"? Partitioning sums of squares or the log likelihood into components, e.g., combined test of interaction and combined test of nonlinearities, is very easy and natural in the frequentist setting.
- How do we specify priors for complex entities such as the degree of monotonicity of the effect of a continuous predictor in a regression model? The Bayesian approach to this will ultimately be more satisfying, but operationalizing this is not easy.