Prediction markets, Bayesian priors, and clinical trials

Statisticians seem to have paid little attention to prediction markets, leading examples of which are the political stock markets run by the University of Iowa. The proponents of prediction markets find their accuracy to be good, a quality that may be due partly to the incentive that they provide. The markets yield ready aggregation of opinions across multiple assessors. They can be used in eliciting statistical distributions of future observed data. This paper examines the possible use of prediction markets to obtain prior distributions for Bayesian inference. Priors can be found by using prediction markets to elicit the distribution of data to be observed and then exploiting the relation between that distribution and the prior. A prior thus obtained can be seen as being, relatively speaking, both objective and informative. The paper includes a number of examples dealing both with the general elicitation of statistical distributions from prediction markets and with the use of prediction markets to get Bayesian priors. Because Bayesian approaches are frequently proposed for use in the area of clinical trials, that area receives specific attention.