Kass and Greenhouse (1989) proposed using "community of priors" (see also Fayers et al, 1997; 2000). As described by Spiegelhalter (2004), they can be seen as a
range of viewpoints that should be considered when interpreting evidence, and therefore a Bayesian analysis is best seen as providing a mapping from a space of specified prior beliefs to appropriate posterior beliefs.
Their main idea was that several different priors can be used to set up different models, so to calculate posterior probabilities when using them. The priors can be based on different beliefs or hypotheses. In decision making scenario, say a clinical trial, models calculated under "skeptical", or "optimistic" priors can be compared. Quoting Spiegelhalter (2004) again:
The community of prior opinions becomes particularly important when faced with the difficult issue of whether to stop a clinical trial. Kass and Greenhouse (1989) express the crucial view that “the purpose of a trial is to collect data that bring to conclusive consensus at termination opinions that had been diverse and indecisive at the outset,” and this idea may be formalized as follows:
- Stopping with a “positive” result (i.e., in favor of the new treatment) might be considered if a posterior based on a sceptical prior suggested a high probability of treatment benefit.
- Stopping with a “negative” result (i.e., equivocal or in favor of the standard treatment) may be based on whether the results were sufficiently disappointing to make a posterior based on an enthusiastic prior rule out a treatment benefit.
In other words we should stop if we have convinced a reasonable adversary that they are wrong.
The idea is appealing, however it is hard to find examples of their usage in real-life research. Do you know any such examples? Why this approach isn't used more commonly?
[Disclosure: This question arose after our recent exchange of arguments with @Aksakal.]
Kass, R.E. and Greenhouse, J.B. (1989). A Bayesian perspective. Comment on “Investigating therapies of potentially great benefit: ECMO,” by J. H. Ware. Statistical Science, 4, 310-317.
Spiegelhalter, D. J. (2004). Incorporating Bayesian ideas into health-care evaluation. Statistical Science, 156-174.
Fayers, P.M., Ashby, D., & Parmar, M.K. (1997). Tutorial in biostatistics Bayesian data monitoring in clinical trials. Statistics in medicine, 16(12), 1413-1430.
Fayers, P.M., Cuschieri, A., Fielding, J., Craven, J., Uscinska, B., & Freedman, L.S. (2000). Sample size calculation for clinical trials: the impact of clinician beliefs. British journal of cancer, 82(1), 213.