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H. Chernoff 33Savage tried to defend his method, but soon gave in with the remark thatperhaps we should examine the work of de Finetti on the Bayesian approachto inference. He later became a sort of high priest in the ensuing controversybetween the Bayesians and the misnamed frequentists. I posed a list of propertiesthat an objective scientist should require of a criterion for decision theoryproblems. There was no criterion satisfying that list in a problem with a finitenumber of states of nature, unless we canceled one of the requirements. Inthat case the only criterion was one of all states being equally likely. To methat meant that there could be no objective way of doing science. I held backpublishing those results for a few years hoping that time would resolve theissue (Chernoff, 1954).In the controversy, I remained a frequentist. My main objection to Bayesianphilosophy and practice was based on the choice of the prior probability. Inprinciple, it should come from the initial belief. Does that come from birth?If we use instead a non-informative prior, the choice of one may carry hiddenassumptions in complicated problems. Besides, the necessary calculationwas very forbidding at that time. The fact that randomized strategies are notneeded for Bayes procedures is disconcerting, considering the important roleof random sampling. On the other hand, frequentist criteria lead to the contradictionof the reasonable criteria of rationality demanded by the derivationof Bayesian theory, and thus statisticians have to be very careful about theuse of frequentist methods.In recent years, my reasoning has been that one does not understand aproblem unless it can be stated in terms of a Bayesian decision problem. If onedoes not understand the problem, the attempts to solve it are like shooting inthe dark. If one understands the problem, it is not necessary to attack it usingBayesian analysis. My thoughts on inference have not grown much since thenin spite of my initial attraction to statistics that came from the philosophicalimpact of Neyman–Pearson and decision theory.One slightly amusing correspondence with de Finetti came from a problemfrom the principal of a local school that had been teaching third gradersSpanish. He brought me some data on a multiple choice exam given to thechildren to evaluate how successful the teaching had been. It was clear fromthe results that many of the children were guessing on some of the questions.Atraditionalwaytocompensateforguessingistosubtractapenaltyforeach wrong answer. But when the students are required to make a choice,this method simply applies a linear transformation to the score and does notprovide any more information than the number of correct answers. I proposeda method (Chernoff, 1962) which turned out to be an early application ofempirical Bayes. For each question, the proportion of correct answers in theclass provides an estimate of how many guessed and what proportion of thecorrect answers were guesses. The appropriate reward for a correct answershould take this estimate into account. Students who hear of this approachare usually shocked because if they are smart, they will suffer if they are in aclass with students who are not bright.