Discussion: Foundations of Statistical Inference, Revisited
نویسندگان
چکیده
This is an invited contribution to the discussion on Professor Deborah Mayo’s paper, “On the Birnbaum argument for the strong likelihood principle,” to appear in Statistical Science. Mayo clearly demonstrates that statistical methods violating the likelihood principle need not violate either the sufficiency or conditionality principle, thus refuting Birnbaum’s claim. With the constraints of Birnbaum’s theorem lifted, we revisit the foundations of statistical inference, focusing on some new foundational principles, the inferential model framework, and connections with sufficiency and conditioning.
منابع مشابه
On the trasductive arguments in statistics
The paper argues that a part of the current statistical discussion is not based on the standard firm foundations of the field. Among the examples we consider are prediction into the future, semi-supervised classification, and causality inference based on observational data.
متن کاملAnother View of the Classical Problem of Comparing Two Probabilities
The usual calculation of the P-value for the classical problem of comparing probabilities is not always accurate. This issue arose in the context of a legal dispute which depended on when some written material was written in a diary. The problem raises some issues on the foundations of statistical inference.
متن کاملI Frequentist Statistics as a Theory of Inductive Inference 1
The philosophical foundations of statistics may be regarded as the study of the epistemological, conceptual, and logical problems revolving around the use and interpretation of statistical methods, broadly conceived. As with other domains of philosophy of science, work in statistical science progresses largely without worrying about “philosophical foundations.” Nevertheless, even in statistical...
متن کاملPhilosophy of Econometrics
1. Introduction 2. What philosophical/methodological issues? 3. Philsophy of science and empirical modeling: Logical positivism/empiricism The downfall of logical positivism/empiricism The new experimentalism Learning from error 4. The Error-Statistical perspective: Statistical inference and its philosophical foundations Statistical Induction and its underlying reasoning Severe testing reasonin...
متن کاملPrinciples of Statistical Inference
Statistical theory aims to provide a foundation for studying the collection and interpretation of data that does not depend on the particular details of the substantive field in which the data is being considered. This gives a systematic way to approach new problems, and a common language for summarizing results; ideally the foundations and common language ensure that statistical aspects of one...
متن کامل