Foundations of statistics

From Wikipedia, the free encyclopedia

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].

Contents 1 Other Reading 2 See also 3 References 4 Further reading 5 External links

[edit] 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.

[edit] See also

• Likelihood principle
• Philosophy of mathematics
• Philosophy of science
• Probability interpretations
• Statistics
• Thomas Bayes
• Andrey Kolmogorov

[edit] References

• Abelson, Robert P. (1995). Statistics as Principled Argument. Lawrence Erlbaum Associates. ISBN 0805805281. “... 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.
• Ord K, Stuart A. (1994), Kendall's Advanced Theory of Statistics, volume I: Distribution Theory (Edward Arnold).

[edit] Further reading

Please expand this article using the suggested source(s) below. More information might be found in a section of the talk page.

• Barnett, Vic (1999), Comparative Statistical Inference (3rd ed.), Wiley, ISBN 978-0471976431 
• Cox, David R. (2006), Principles of Statistical Inference, Cambridge University Press, ISBN 978-0521685672 
• Efron, Bradley (1986), “Why Isn't Everyone a Bayesian? (with discussion)”, American Statistician 40 (1): 1-11, <http://links.jstor.org/sici?sici=0003-1305%28198602%2940%3A1%3C1%3AWIEAB%3E2.0.CO%3B2-3> 
• Good, I. J. (1988), “The Interface Between Statistics and Philosophy of Science”, Statistical Science 3 (4): 386-397, <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.]
• Lindley, D.V. (2000), “The philosophy of statistics”, Journal of the Royal Statistical Society: Series D 49: 293–337, DOI 10.1111/1467-9884.00238 
• Mayo, Deborah G. (1992), “Did Pearson reject the Neyman-Pearson philosophy of statistics?”, Synthese 90: 233-262, DOI 10.1007/BF00485352 
• Royall, Richard M. (1997), Statistical Evidence: A Likelihood Paradigm, CRC Press, ISBN 0412044110 
• Savage L.J. (1972), The Foundations of Statistics (Dover).

[edit] External links

• Citations of Savage (1972) at Citeseer. [Over 250 citations.]
• Disputes in statistical analyses a single-page review, from an elementary perspective.
• Stanford Encyclopedia of Philosophy entry on probability interpretations.