Foundations of statistics

Foundations of statistics is the usual name for the epistemological debate over how one should conduct inductive inference from data. Among issues considered are the question of Bayesian inference versus frequentist inference, the distinction between Fisher's "significance testing" and Neyman-Pearson "hypothesis testing", and whether the likelihood principle should be followed. Some of these issues have been debated for up to 200 years without resolution [Efron, 1978] .

Other Reading

For a short introduction to the foundations of statistics, see ch. 6 ("Probability and statistical inference") of "Kendall's Advanced Theory of Statistics" (6th edition, 1994).

In his book "Statistics As Principled Argument", Robert P. Abelson articulates the position that statistics serves as a standardized means of settling disputes between scientists who could otherwise each argue the merits of their own positions "ad infinitum". From this point of view, statistics is a form of rhetoric; as with any means of settling disputes, statistical methods can succeed only as long as all parties agree on the approach used.

ee also

*Philosophy of statistics
*Statistics
*History of statistics
*Induction
*Data Analysis
*Philosophy of probability
*Philosophy of mathematics
*Philosophy of science
*Evidence
*Bayesian Inference
*Degrees of Certainty
*Scientific method
*Probability interpretations
*Likelihood principle

Notable People

*Thomas Bayes
*Andrey Kolmogorov
*Ian Hacking
*Bradley Efron
*I. J. Good
*R. A. Fisher
*Karl Pearson

References

*cite book |last=Abelson |first=Robert P. |authorlink=Robert P. Abelson |title=Statistics as Principled Argument |year=1995 |publisher=Lawrence Erlbaum Associates |isbn=0805805281 |quote=... the purpose of statistics is to organize a useful argument from quantitative evidence, using a form of principled rhetoric.
*Efron B. (1978), "Controversies in the foundations of statistics", "American Mathematical Monthly", 85: 231-246.
*Stuart A., Ord J.K. (1994), "Kendall's Advanced Theory of Statistics, volume I: Distribution Theory" (Edward Arnold).

Further reading

*Citation | last=Barnett | first=Vic | year=1999 | title=Comparative Statistical Inference | edition= 3rd| publisher=Wiley | isbn=978-0471976431
*Citation | last=Cox | first = David R. | author-link=David Cox (statistician)| title=Principles of Statistical Inference | publisher=Cambridge University Press | year=2006|isbn=978-0521685672
*Citation | last= Efron | first=Bradley | author-link=Bradley Efron | title=Why Isn't Everyone a Bayesian? (with discussion)| journal= American Statistician | volume= 40 | number= 1 | year=1986 | pages= 1-11 | url=http://links.jstor.org/sici?sici=0003-1305%28198602%2940%3A1%3C1%3AWIEAB%3E2.0.CO%3B2-3
*Citation| last=Good | first=I. J.| title=The Interface Between Statistics and Philosophy of Science | journal=Statistical Science | volume= 3| number=4 | year=1988 |pages=386-397 | url=http://links.jstor.org/sici?sici=0883-4237%28198811%293%3A4%3C386%3ATIBSAP%3E2.0.CO%3B2-I
*Kadane J.B., Schervish M.J., Seidenfeld T. (1999), "Rethinking the Foundations of Statistics" (Cambridge University Press). [Bayesian.]
*Citation|last=Lindley |first=D.V.| author-link=Dennis Lindley |year=2000| title=The philosophy of statistics| journal=Journal of the Royal Statistical Society: Series D| volume=49| pages=293–337|doi=10.1111/1467-9884.00238
*Citation| last=Mayo |first=Deborah G.| title=Did Pearson reject the Neyman-Pearson philosophy of statistics? | journal=Synthese |volume=90 |pages=233-262 |year= 1992 | doi=10.1007/BF00485352
*Citation| last=Royall | first=Richard M. | title=Statistical Evidence: A Likelihood Paradigm |publisher=CRC Press | isbn=0412044110 | year=1997
*Savage L.J. (1972), "The Foundations of Statistics" (Dover Publications).

External links

* [http://citeseer.comp.nus.edu.sg/context/6790/0 Citations of Savage (1972)] at Citeseer. [Over 250 citations.]
*Stanford Encyclopedia of Philosophy [http://plato.stanford.edu/entries/probability-interpret/ entry] on probability interpretations.