On the Mathematical Foundations of Theoretical Statistics.¶
Fisher, R. A. (1922). On the Mathematical Foundations of Theoretical Statistics. Philosophical Transactions of the Royal Society of London, Series A, 222(594–604), 594-604.
Cited by¶
3 citations across 3 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Bias
- Formally, as Fisher (1922) framed in his foundational paper on the mathematical foundations of theoretical statistics, an estimating procedure has a bias equal to the difference between the expected value of its output and the quantity it is meant to recover; that difference survives the limit of infinitely many observations.
This sourceFoundational formalization of estimation (consistency, efficiency, sufficiency, likelihood): an estimating procedure's bias is the difference between the expected value of its statistic and the target parameter — a property of the procedure that survives the infinite-sample limit and travels from estimation theory into measurement, cognition, machine learning, and institutions.
- Formally, as Fisher (1922) framed in his foundational paper on the mathematical foundations of theoretical statistics, an estimating procedure has a bias equal to the difference between the expected value of its output and the quantity it is meant to recover; that difference survives the limit of infinitely many observations.
- Conditional Probability
- Recognizing the conditional-probability pattern enables several portable moves. Direction inversion via Bayes: any forward conditional — symptom given disease, evidence given guilt, data given parameter — can be inverted to the diagnostic or posterior conditional given a prior, a move that is structural while the substrate varies. Conditional independence as factorization: complex joints factor along their conditional-independence structure, so the diagnostic "given \(C\), are \(A\) and \(B\) independent?" directly reduces the dimensional explosion. Sufficient statistics: a sufficient statistic captures all the information a sample carries about a parameter, which is structurally the conditional-independence claim that the parameter depends on the data only through the statistic
This sourceIntroduces sufficiency — a sufficient statistic captures all sample information about a parameter, structurally a conditional-independence claim.
- Recognizing the conditional-probability pattern enables several portable moves. Direction inversion via Bayes: any forward conditional — symptom given disease, evidence given guilt, data given parameter — can be inverted to the diagnostic or posterior conditional given a prior, a move that is structural while the substrate varies. Conditional independence as factorization: complex joints factor along their conditional-independence structure, so the diagnostic "given \(C\), are \(A\) and \(B\) independent?" directly reduces the dimensional explosion. Sufficient statistics: a sufficient statistic captures all the information a sample carries about a parameter, which is structurally the conditional-independence claim that the parameter depends on the data only through the statistic
- Feature Engineering
- And classical statistics supplies a limiting case: the optimally engineered feature for a known model family is the sufficient statistic.
This sourceIntroduces sufficiency and the sufficient statistic — the limiting case of an optimally engineered feature for a known model family, supporting the sufficient-statistic anchor.
- And classical statistics supplies a limiting case: the optimally engineered feature for a known model family is the sufficient statistic.
Verification¶
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