@article{Frosini_2008, title={On some counter-counter-examples about classical inference}, volume={68}, url={https://rivista-statistica.unibo.it/article/view/3526}, DOI={10.6092/issn.1973-2201/3526}, abstractNote={This paper deals with theoretical concepts and practical examples, aimed at showing that non-Bayesian inference is liable to result in mistakes or unacceptable conclusions, and proves that they are not justified. Section 2 comments on examples when an objective prior distribution exists, and shows how widely one can be mistaken in using a prior quite distant from the real one. Section 3 comments on two results by Godambe, stressing that – in sampling from finite populations – no flat likelihood exists, while an unbiased linear “estimator” with zero variance does not exist, unless we reach a complete knowledge of the population. Section 4 stresses the fundamental difference between a “probability interval” for a parameter, and a “confidence interval” aimed at making inference on the parameter, thus summarizing all certain facts and constraints able to shrink such an inferential interval. Section 5 explains why we are justified in attaching an inductive meaning to a realized confidence interval. Finally, Section 6 counters some well known counter-examples spread in the Bayesian literature, showing that they are unacceptable from a sound inductive basis.}, number={2}, journal={Statistica}, author={Frosini, Benito Vittorio}, year={2008}, month={Jan.}, pages={135–152} }