Foundations of statistics
Encyclopedia
Foundations of statistics is the usual name for the epistemological debate in statistics
over how one should conduct inductive inference
from data. Among the issues considered in statistical inference
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].
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.
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
over how one should conduct inductive inference
Inductive inference
Around 1960, Ray Solomonoff founded the theory of universal inductive inference, the theory of prediction based on observations; for example, predicting the next symbol based upon a given series of symbols...
from data. Among the issues considered in statistical inference
Statistical inference
In statistics, statistical inference is the process of drawing conclusions from data that are subject to random variation, for example, observational errors or sampling variation...
are the question of Bayesian inference
Bayesian inference
In statistics, Bayesian inference is a method of statistical inference. It is often used in science and engineering to determine model parameters, make predictions about unknown variables, and to perform model selection...
versus frequentist inference
Frequentist inference
Frequentist inference is one of a number of possible ways of formulating generally applicable schemes for making statistical inferences: that is, for drawing conclusions from statistical samples. An alternative name is frequentist statistics...
, the distinction between Fisher
Ronald Fisher
Sir Ronald Aylmer Fisher FRS was an English statistician, evolutionary biologist, eugenicist and geneticist. Among other things, Fisher is well known for his contributions to statistics by creating Fisher's exact test and Fisher's equation...
's "significance testing" and Neyman
Jerzy Neyman
Jerzy Neyman , born Jerzy Spława-Neyman, was a Polish American mathematician and statistician who spent most of his professional career at the University of California, Berkeley.-Life and career:...
-Pearson
Egon Pearson
Egon Sharpe Pearson, CBE FRS was the only son of Karl Pearson, and like his father, a leading British statistician....
"hypothesis testing", and whether the likelihood principle
Likelihood principle
In statistics,the likelihood principle is a controversial principle of statistical inference which asserts that all of the information in a sample is contained in the likelihood function....
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. 8 ("Probability and statistical inference") of Kendall's Advanced Theory of Statistics (6th edition, 1994).In his book Statistics As Principled Argument, Robert P. Abelson
Robert P. Abelson
Robert Paul Abelson was a Yale University psychologist and political scientist with special interests in statistics and logic....
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
Ad infinitum
Ad infinitum is a Latin phrase meaning "to infinity."In context, it usually means "continue forever, without limit" and thus can be used to describe a non-terminating process, a non-terminating repeating process, or a set of instructions to be repeated "forever," among other uses...
. 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.
See also
- Philosophy of statisticsPhilosophy of statisticsThe philosophy of statistics involves the meaning, justification, utility, use and abuse of statistics and its methodology, and ethical and epistemological issues involved in the consideration of choice and interpretation of data and methods of Statistics....
- History of statisticsHistory of statisticsThe history of statistics can be said to start around 1749 although, over time, there have been changes to the interpretation of what the word statistics means. In early times, the meaning was restricted to information about states...
- Philosophy of probability
- Philosophy of mathematicsPhilosophy of mathematicsThe philosophy of mathematics is the branch of philosophy that studies the philosophical assumptions, foundations, and implications of mathematics. The aim of the philosophy of mathematics is to provide an account of the nature and methodology of mathematics and to understand the place of...
- Philosophy of sciencePhilosophy of scienceThe philosophy of science is concerned with the assumptions, foundations, methods and implications of science. It is also concerned with the use and merit of science and sometimes overlaps metaphysics and epistemology by exploring whether scientific results are actually a study of truth...
- EvidenceEvidenceEvidence in its broadest sense includes everything that is used to determine or demonstrate the truth of an assertion. Giving or procuring evidence is the process of using those things that are either presumed to be true, or were themselves proven via evidence, to demonstrate an assertion's truth...
- Probability interpretationsProbability interpretationsThe word probability has been used in a variety of ways since it was first coined in relation to games of chance. Does probability measure the real, physical tendency of something to occur, or is it just a measure of how strongly one believes it will occur? In answering such questions, we...
- Founders of statisticsFounders of statisticsStatistics is the theory and application of mathematics to the scientific method including hypothesis generation, experimental design, sampling, data collection, data summarization, estimation, prediction and inference from those results to the population from which the experimental sample was drawn...
Further reading
- Kadane J.B., Schervish M.J., Seidenfeld T. (1999), Rethinking the Foundations of Statistics (Cambridge University PressCambridge University PressCambridge University Press is the publishing business of the University of Cambridge. Granted letters patent by Henry VIII in 1534, it is the world's oldest publishing house, and the second largest university press in the world...
). [Bayesian.]
External links
- Citations of Savage (1972) at CiteseerCiteSeerCiteSeer was a public search engine and digital library for scientific and academic papers. It is often considered to be the first automated citation indexing system and was considered a predecessor of academic search tools such as Google Scholar and Microsoft Academic Search. It was replaced by...
. [Over 250 citations.] - Stanford Encyclopedia of Philosophy entry on probability interpretations.