The application of mathematical probability theory in statistics is quite controversial. Controversies regard both the interpretation of probability and approaches to statistical inference. After having given an overview of the main approaches, I will propose a re-interpretation of frequentist probability. Most statisticians are aware that probability models interpreted in a frequentist manner are not really true in objective reality, but only idealizations. I argue that this is often ignored when actually applying frequentist methods and interpreting the results, and that keeping up the awareness for the essential difference between reality and models can lead to a more appropriate use and interpretation of frequentist models and methods, called “frequentism-as-model.” This is elaborated showing connections to existing work, appreciating the special role of independently and identically distributed observations and subject matter knowledge, giving an account of how and under what conditions models that are not true can be useful, giving detailed interpretations of tests and confidence intervals, confronting their implicit compatibility logic with the inverse probability logic of Bayesian inference, re-interpreting the role of model assumptions, and appreciating robustness and the role of “interpretative equivalence” of models. Epistemic probability shares the issue that its models are only idealizations, and an analogous “epistemic-probability-as-model” can also be developed.

Hennig, C. (2023). Probability Models in Statistical Data Analysis: Uses, Interpretations, Frequentism-as-Model. Cham : Bharath Sriraman [10.1007/978-3-030-19071-2_105-1].

Probability Models in Statistical Data Analysis: Uses, Interpretations, Frequentism-as-Model

Hennig, Christian
Primo
2023

Abstract

The application of mathematical probability theory in statistics is quite controversial. Controversies regard both the interpretation of probability and approaches to statistical inference. After having given an overview of the main approaches, I will propose a re-interpretation of frequentist probability. Most statisticians are aware that probability models interpreted in a frequentist manner are not really true in objective reality, but only idealizations. I argue that this is often ignored when actually applying frequentist methods and interpreting the results, and that keeping up the awareness for the essential difference between reality and models can lead to a more appropriate use and interpretation of frequentist models and methods, called “frequentism-as-model.” This is elaborated showing connections to existing work, appreciating the special role of independently and identically distributed observations and subject matter knowledge, giving an account of how and under what conditions models that are not true can be useful, giving detailed interpretations of tests and confidence intervals, confronting their implicit compatibility logic with the inverse probability logic of Bayesian inference, re-interpreting the role of model assumptions, and appreciating robustness and the role of “interpretative equivalence” of models. Epistemic probability shares the issue that its models are only idealizations, and an analogous “epistemic-probability-as-model” can also be developed.
2023
Handbook of the History and Philosophy of Mathematical Practice
1
49
Hennig, C. (2023). Probability Models in Statistical Data Analysis: Uses, Interpretations, Frequentism-as-Model. Cham : Bharath Sriraman [10.1007/978-3-030-19071-2_105-1].
Hennig, Christian
File in questo prodotto:
Eventuali allegati, non sono esposti

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/949303
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact