ABSTRACT
All over the world, every day, scientists throw away information. Sometimes this is through the removal of "outliers" cases in the data that offend the model and so are exiled. It is easy to retain the information about sample size. All that is needed is to model what has actually been observed, the counts instead of the proportions. No one has ever observed a proportion. Instead people observe counts. The experimental structure mimics many common experiments conducted on human students by economists and psychologists. When either the left or right lever is pulled by the focal animal, the two dishes on the same side slide towards opposite ends of the table. This delivers whatever is in those dishes to the opposite ends. In all experimental trials, both dishes on the focal animal's side contain food items. The only reason the posterior distribution falls off at all is because we used a weak regularizing prior in the model definition.
