In statistical inference, there are many fundamental statistical principles, such as likelihood principle and repeated sampling principle. I am wondering whether there are any other principles? And what's the meaning of these principles? What's the difference between these principles, especially between likelihood principle and repeated sampling principle?

From the book "Likelihood Methods in Statistics" by T.A.Severini, "the repeated sampling principle states that statistical procedures should be evaluated on the basis of their behavior in hypothetical repetitions of the experiment that generated the original data. Of course, there is considerable arbitrariness in how this principle is interpreted, in particular, in how the hypothetical repetitions are defined. The basic idea however, which is simply that a given statistical procedure should be evaluated based on how it would perform inf adopted for routine use, is certainly reasonable."

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    $\begingroup$ To keep this question on topic, we will need to keep it focused on comparing the "likelihood principle" and the "repeated sampling principle": answering it in full generality requires a several-volume text. But I suspect I'm not alone in wondering precisely what you mean by the "repeated sampling principle." Could you please indicate what you understand these principles to mean, or at least provide links to the definitions you intend to use? $\endgroup$
    – whuber
    Feb 10, 2012 at 3:53
  • $\begingroup$ Thanks. I added the definition from the book I mentioned. $\endgroup$ Feb 10, 2012 at 4:39
  • $\begingroup$ @HonglangWang I believe that the repeated sampling principle is more related to the repeatability required by the 'classical approach'. The likelihood principle states that all the information in a sample is contained in the likelihood. It follows from the conditionality principle and the sufficiency principle. If you are interested on this topic I would recommend you The Likelihood Principle by Berger and Wolpert. $\endgroup$
    – user10525
    May 17, 2012 at 22:19

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You can find an extensive set of principles and the like in chapter 2 of Cox and Hinkley, Theoretical Statistics (1974). They have sections for: The likelihood (sic?); Sufficient statistics; Completeness; Ancillary statistics; Asymptotic sufficiency; Sufficiency principle; Conditionality principle; Weak likelihood principle; Strong likelihood principle; Invariance principle; Strong repeated sampling principle; Weak repeated sampling principle; Bayesian coherency principle; Principle of coherent decision making; Sampling theory; Likelihood theory; Bayesian theory; and Decision theory.


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