Philosophy of statistics

Foundations of statistics

The foundations of statistics concern 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. Bandyopadhyay & Forster describe four statistical paradigms: "(i) classical statistics or error statistics, (ii) Bayesian statistics, (iii) likelihood-based statistics, and (iv) the Akaikean-Information Criterion-based statistics". Leonard J. Savage's widely cited text Foundations of Statistics states: It is unanimously agreed that statistics depends somehow on probability. But, as to what probability is and how it is connected with statistics, there has seldom been such complete disagreement and breakdown of communication since the Tower of Babel. Doubtless, much of the disagreement is merely terminological and would disappear under sufficiently sharp analysis. (Wikipedia).

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From playlist Introduction to Data Science - Foundations

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From playlist Math Foundations

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From playlist Introduction to Data Science - Foundations

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Related pages

Bayes' theorem | Likelihood principle | Correlation does not imply causation | Statistics | Harold Jeffreys | Modus tollens | Philosophy of statistics | All models are wrong | Akaike information criterion | Statistical model | Likelihoodist statistics | Ad infinitum | Neyman–Pearson lemma | Statistical inference | Sample size determination | Student's t-test | History of statistics | Founders of statistics | Jerzy Neyman | Likelihood function | Leonard Jimmie Savage | Inductive reasoning | Statistical hypothesis testing | Principle of indifference | Bruno de Finetti | George E. P. Box | Fiducial inference | Probability interpretations | Bayesian inference | Philosophy of mathematics | Frequentist inference