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In statistical practice, whether a Bayesian or frequentist approach is usedin inference depends not only on the availability of prior information but alsoon the attitude taken toward partial prior information, with frequentiststending to be more cautious than Bayesians. The proposed framework defines thatattitude in terms of a specified amount of caution, thereby enabling dataanalysis at the level of caution desired and on the basis of any priorinformation. The caution parameter represents the attitude toward partial priorinformation in much the same way as a loss function represents the attitudetoward risk. When there is very little prior information and nonzero caution,the resulting inferences correspond to those of the candidate confidenceintervals and p-values that are most similar to the credible intervals andhypothesis probabilities of the specified Bayesian posterior. On the otherhand, in the presence of a known physical distribution of the parameter,inferences are based only on the corresponding physical posterior. In thoseextremes of either negligible prior information or complete prior information,inferences do not depend on the degree of caution. Partial prior informationbetween those two extremes leads to intermediate inferences that are morefrequentistic to the extent that the caution is high and more Bayesian to theextent that the caution is low.

Controlling the degree of caution in statistical inference with the Bayesian and frequentist approaches as opposite extremes