- See Also
-
Gwern
- “Statistical Notes”, Gwern 2014
- “Open Questions”, Gwern 2018
- “Calculating The Gaussian Expected Maximum”, Gwern 2016
- “Dog Cloning For Special Forces: Breed All You Can Breed”, Gwern 2018
- “Common Selection Scenarios”, Gwern 2021
- “Embryo Selection For Intelligence”, Gwern 2016
- “Genius Revisited Revisited”, Gwern 2016
- “The Explore-Exploit Dilemma in Media Consumption”, Gwern 2016
- “History of Iterated Embryo Selection”, Gwern 2019
- “Life Extension Cost-Benefits”, Gwern 2015
- “Conscientiousness & Online Education”, Gwern 2012
- “Leaky Pipelines”, Gwern 2014
-
Links
- “The Number of ‘Exceptional’ People: Fewer Than 85 per 1 Million across Key Traits”, Gignac 2025
- “The Global Pattern of Centenarians Highlights Deep Problems in Demography”, Newman 2024
- “Variance Matters More Than Mean in the Extremes”, Cook 2024
- “The Hacker Who Hunts Video Game Speedrunning Cheaters”
- “Scientific Productivity As a Random Walk”, Zhang et al 2023
- “Is Target-Based Drug Discovery Efficient? Discovery and ‘Off-Target’ Mechanisms of All Drugs”, Sadri 2023
- “Power Law Trends in Speedrunning and Machine Learning”, Erdil & Sevilla 2023
- “Distinct Elements in Streams: An Algorithm for the (Text) Book”, Chakraborty et al 2023
- “Scaling Laws for Reward Model Overoptimization”, Gao et al 2022
- “Accurate Detection of Shared Genetic Architecture from GWAS Summary Statistics in the Small-Sample Context”, Willis & Wallace 2022
- “Predictive Validity in Drug Discovery: What It Is, Why It Matters and How to Improve It”, Scannell et al 2022
- “What Was Not Said and What to Do About It”, Kuncel & Worrell 2022
- “Improving Graduate-School Admissions by Expanding Rather Than Eliminating Predictors”, Nye & Ryan 2022
- “Bias, Fairness, and Validity in Graduate-School Admissions: A Psychometric Perspective”, Woo et al 2022
- “The Promise of Potential: A Study on the Effectiveness of Jury Selection to a Prestigious Visual Arts Program”, Kackovic et al 2022
- “Effective Mutation Rate Adaptation through Group Elite Selection”, Kumar et al 2022
- “Assessing the Response to Genomic Selection by Simulation”, Buntaran et al 2022
- “On Extensions of Rank Correlation Coefficients to Multivariate Spaces”, Han 2021
- “A Review of the Gumbel-Max Trick and Its Extensions for Discrete Stochasticity in Machine Learning”, Huijben et al 2021
- “Human Mortality at Extreme Age”, Belzile et al 2021
- “On Boosting the Power of Chatterjee’s Rank Correlation”, Lin & Han 2021
- “Artificial Intelligence in Drug Discovery: What Is Realistic, What Are Illusions? Part 1: Ways to Make an Impact, and Why We Are Not There Yet: Quality Is More Important Than Speed and Cost in Drug Discovery”, Bender & Cortés-Ciriano 2021
- “Recipes and Economic Growth: A Combinatorial March Down an Exponential Tail”, Jones 2021
- “Counterproductive Altruism: The Other Heavy Tail”, Kokotajlo & Oprea 2020
- “A New Coefficient of Correlation: Supplementary Material: Proofs”, Chatterjee 2020
- “A New Coefficient of Correlation”, Chatterjee 2020
- “Supercentenarian and Remarkable Age Records Exhibit Patterns Indicative of Clerical Errors and Pension Fraud”, Newman 2020
- “A Simple Measure of Conditional Dependence”, Azadkia & Chatterjee 2019
- “Low Base Rates Prevented Terman from Identifying Future Nobelists”, Warne et al 2019
- “Scale-Free Networks Are Rare”, Broido & Clauset 2019
- “Test Driving ‘Power of Two Random Choices’ Load Balancing”, Tarreau 2019
- “Right-Tail Range Restriction: A Lurking Threat to Detecting Associations between Traits and Skill among Experts”, Kell & Wai 2019
- “Nature vs. Nurture: Have Performance Gaps Between Men and Women Reached an Asymptote?”, Millard-Stafford et al 2018
- “Categorizing Variants of Goodhart’s Law”, Manheim & Garrabrant 2018
- “Innovation and Cumulative Culture through Tweaks and Leaps in Online Programming Contests”, Miu et al 2018
- “Is Individual Job Performance Distributed According to a Power Law? A Review of Methods for Comparing Heavy-Tailed Distributions”, Spain et al 2017
- “When Quality Beats Quantity: Decision Theory, Drug Discovery, and the Reproducibility Crisis”, Scannell & Bosley 2016
- “Comparing the Pearson and Spearman Correlation Coefficients across Distributions and Sample Sizes: A Tutorial Using Simulations and Empirical Data”, Winter et al 2016
- “Why the Tails Come Apart”, Thrasymachus 2014
- “The Discovery of First-In-Class Drugs: Origins and Evolution”, Eder et al 2014
- “Spearman’s Rho for the AMH Copula: a Beautiful Formula”, Machler 2014
- “The Best And The Rest: Revisiting The Norm Of Normality Of Individual Performance”, O’Boyle & Aguinis 2012
- “A Copula-Based Non-Parametric Measure of Regression Dependence”, Dette et al 2012
- “On the Distribution of Time-To-Proof of Mathematical Conjectures”, Hisano & Sornette 2012
- “How Were New Medicines Discovered?”, Swinney & Anthony 2011
- “A New Car-Following Model Yielding Log-Normal Type Headways Distributions”, Li et al 2010
- “Power-Law Distributions in Empirical Data”, Clauset et al 2007
- “The Major Role of Clinicians in the Discovery of Off-Label Drug Therapies”, DeMonaco et al 2006
- “Copula Associated to Order Statistics”, Anjos et al 2005
- “Computing the Distribution and Expected Value of the Concomitant Rank-Order Statistics”, Barakat & El-Shandidy 2004
- “Accurate Approximation to the Extreme Order Statistics of Gaussian Samples”, Chen & Tyler 1999
- “Research, Patenting, and Technological Change”, Kortum 1997
- “Seeing The Forest From The Trees: When Predicting The Behavior Or Status Of Groups, Correlate Means”, Lubinski & Humphreys 1996b
- “The Relevance of Group Membership for Personnel Selection: A Demonstration Using Bayes’ Theorem”, Miller 1994
- “Validity of the GRE without Restriction of Range”, Huitema & Stein 1993
- “Fairness in Employment Testing: Validity Generalization, Minority Issues, and the General Aptitude Test Battery”, Hartigan & Wigdor 1989
- “Maxima of Normal Random Vectors: Between Independence and Complete Dependence”, Hüsler & Reiss 1989
- “Forecasting Records by Maximum Likelihood”, Smith 1988
- “The Asymptotic Theory of Extreme Order Statistics, Second Edition”, Galambos 1987
- “An Examination of Two Alternative Techniques to Estimate the Standard Deviation of Job Performance in Dollars”, Reilly & Smither 1985
- “Expected Normal Order Statistics (Exact and Approximate)”, Royston 1982
- “Impact of Valid Selection Procedures on Work-Force Productivity”, Schmidt et al 1979
- “How Deviant Can You Be?”, Samuelson 1968
- “Asymptotic Independence of Certain Statistics Connected With the Extreme Order Statistics in a Bivariate Distribution”, Srivastava 1967
- “Estimating Bounds on Athletic Performance”, Deakin 1967
- “Asymptotic Independence of Bivariate Extremes”, Mardia 1964
- “Expected Values of Normal Order Statistics”, Harter 1961
- “Bivariate Extreme Statistics, I”, Sibuya 1960
- “Statistical Estimates and Transformed Beta-Variables”, Blom 1958
- “On the Statistics of Individual Variations of Productivity in Research Laboratories”, Shockley 1957
- “The Asymptotical Distribution of Range in Samples from a Normal Population”, Elfving 1947
- “The Relationship Of Validity Coefficients To The Practical Effectiveness Of Tests In Selection: Discussion And Tables”
- “Statistical Method”, Kelley 1923
- “How Many Hottest Days of the Year (So Far)?”
- “What Does It Mean to Have a Low R-Squared? A Warning about Misleading Interpretation”
- “Approximate Order Statistics for Normal Random Variables”
- “Univariate Distributional Analysis With L-Moment Statistics Using R”
- “Modelling a Time Series of Records With PyMC3”
- “Rényi’s Parking Constant”
- “Analyzing DeepMind’s Probabilistic Methods for Evaluating Agent Capabilities”
- Wikipedia
- Miscellaneous
- Bibliography
See Also
Gwern
“Statistical Notes”, Gwern 2014
“Open Questions”, Gwern 2018
“Calculating The Gaussian Expected Maximum”, Gwern 2016
“Dog Cloning For Special Forces: Breed All You Can Breed”, Gwern 2018
“Common Selection Scenarios”, Gwern 2021
“Embryo Selection For Intelligence”, Gwern 2016
“Genius Revisited Revisited”, Gwern 2016
“The Explore-Exploit Dilemma in Media Consumption”, Gwern 2016
“History of Iterated Embryo Selection”, Gwern 2019
“Life Extension Cost-Benefits”, Gwern 2015
“Conscientiousness & Online Education”, Gwern 2012
“Leaky Pipelines”, Gwern 2014
Links
“The Number of ‘Exceptional’ People: Fewer Than 85 per 1 Million across Key Traits”, Gignac 2025
The number of ‘exceptional’ people: Fewer than 85 per 1 million across key traits
“The Global Pattern of Centenarians Highlights Deep Problems in Demography”, Newman 2024
The global pattern of centenarians highlights deep problems in demography
“Variance Matters More Than Mean in the Extremes”, Cook 2024
“The Hacker Who Hunts Video Game Speedrunning Cheaters”
“Scientific Productivity As a Random Walk”, Zhang et al 2023
“Is Target-Based Drug Discovery Efficient? Discovery and ‘Off-Target’ Mechanisms of All Drugs”, Sadri 2023
Is Target-Based Drug Discovery Efficient? Discovery and ‘Off-Target’ Mechanisms of All Drugs
“Power Law Trends in Speedrunning and Machine Learning”, Erdil & Sevilla 2023
“Distinct Elements in Streams: An Algorithm for the (Text) Book”, Chakraborty et al 2023
Distinct Elements in Streams: An Algorithm for the (Text) Book
“Scaling Laws for Reward Model Overoptimization”, Gao et al 2022
“Accurate Detection of Shared Genetic Architecture from GWAS Summary Statistics in the Small-Sample Context”, Willis & Wallace 2022
“Predictive Validity in Drug Discovery: What It Is, Why It Matters and How to Improve It”, Scannell et al 2022
Predictive validity in drug discovery: what it is, why it matters and how to improve it:
View PDF:
“What Was Not Said and What to Do About It”, Kuncel & Worrell 2022
“Improving Graduate-School Admissions by Expanding Rather Than Eliminating Predictors”, Nye & Ryan 2022
Improving Graduate-School Admissions by Expanding Rather Than Eliminating Predictors
“Bias, Fairness, and Validity in Graduate-School Admissions: A Psychometric Perspective”, Woo et al 2022
Bias, Fairness, and Validity in Graduate-School Admissions: A Psychometric Perspective
“The Promise of Potential: A Study on the Effectiveness of Jury Selection to a Prestigious Visual Arts Program”, Kackovic et al 2022
“Effective Mutation Rate Adaptation through Group Elite Selection”, Kumar et al 2022
Effective Mutation Rate Adaptation through Group Elite Selection
“Assessing the Response to Genomic Selection by Simulation”, Buntaran et al 2022
“On Extensions of Rank Correlation Coefficients to Multivariate Spaces”, Han 2021
On extensions of rank correlation coefficients to multivariate spaces
“A Review of the Gumbel-Max Trick and Its Extensions for Discrete Stochasticity in Machine Learning”, Huijben et al 2021
A Review of the Gumbel-max Trick and its Extensions for Discrete Stochasticity in Machine Learning
“Human Mortality at Extreme Age”, Belzile et al 2021
“On Boosting the Power of Chatterjee’s Rank Correlation”, Lin & Han 2021
“Artificial Intelligence in Drug Discovery: What Is Realistic, What Are Illusions? Part 1: Ways to Make an Impact, and Why We Are Not There Yet: Quality Is More Important Than Speed and Cost in Drug Discovery”, Bender & Cortés-Ciriano 2021
“Recipes and Economic Growth: A Combinatorial March Down an Exponential Tail”, Jones 2021
Recipes and Economic Growth: A Combinatorial March Down an Exponential Tail
“Counterproductive Altruism: The Other Heavy Tail”, Kokotajlo & Oprea 2020
“A New Coefficient of Correlation: Supplementary Material: Proofs”, Chatterjee 2020
A New Coefficient of Correlation: Supplementary material: Proofs:
“A New Coefficient of Correlation”, Chatterjee 2020
“Supercentenarian and Remarkable Age Records Exhibit Patterns Indicative of Clerical Errors and Pension Fraud”, Newman 2020
“A Simple Measure of Conditional Dependence”, Azadkia & Chatterjee 2019
“Low Base Rates Prevented Terman from Identifying Future Nobelists”, Warne et al 2019
Low Base Rates Prevented Terman from Identifying Future Nobelists
“Scale-Free Networks Are Rare”, Broido & Clauset 2019
“Test Driving ‘Power of Two Random Choices’ Load Balancing”, Tarreau 2019
“Right-Tail Range Restriction: A Lurking Threat to Detecting Associations between Traits and Skill among Experts”, Kell & Wai 2019
“Nature vs. Nurture: Have Performance Gaps Between Men and Women Reached an Asymptote?”, Millard-Stafford et al 2018
Nature vs. Nurture: Have Performance Gaps Between Men and Women Reached an Asymptote?
“Categorizing Variants of Goodhart’s Law”, Manheim & Garrabrant 2018
“Innovation and Cumulative Culture through Tweaks and Leaps in Online Programming Contests”, Miu et al 2018
Innovation and cumulative culture through tweaks and leaps in online programming contests
“Is Individual Job Performance Distributed According to a Power Law? A Review of Methods for Comparing Heavy-Tailed Distributions”, Spain et al 2017
“When Quality Beats Quantity: Decision Theory, Drug Discovery, and the Reproducibility Crisis”, Scannell & Bosley 2016
When Quality Beats Quantity: Decision Theory, Drug Discovery, and the Reproducibility Crisis
“Comparing the Pearson and Spearman Correlation Coefficients across Distributions and Sample Sizes: A Tutorial Using Simulations and Empirical Data”, Winter et al 2016
View PDF:
“Why the Tails Come Apart”, Thrasymachus 2014
“The Discovery of First-In-Class Drugs: Origins and Evolution”, Eder et al 2014
The discovery of first-in-class drugs: origins and evolution
“Spearman’s Rho for the AMH Copula: a Beautiful Formula”, Machler 2014
“The Best And The Rest: Revisiting The Norm Of Normality Of Individual Performance”, O’Boyle & Aguinis 2012
The Best And The Rest: Revisiting The Norm Of Normality Of Individual Performance
“A Copula-Based Non-Parametric Measure of Regression Dependence”, Dette et al 2012
A Copula-Based Non-parametric Measure of Regression Dependence
“On the Distribution of Time-To-Proof of Mathematical Conjectures”, Hisano & Sornette 2012
On the distribution of time-to-proof of mathematical conjectures
“How Were New Medicines Discovered?”, Swinney & Anthony 2011
“A New Car-Following Model Yielding Log-Normal Type Headways Distributions”, Li et al 2010
A new car-following model yielding log-normal type headways distributions
“Power-Law Distributions in Empirical Data”, Clauset et al 2007
“The Major Role of Clinicians in the Discovery of Off-Label Drug Therapies”, DeMonaco et al 2006
The Major Role of Clinicians in the Discovery of Off-Label Drug Therapies
“Copula Associated to Order Statistics”, Anjos et al 2005
“Computing the Distribution and Expected Value of the Concomitant Rank-Order Statistics”, Barakat & El-Shandidy 2004
Computing the Distribution and Expected Value of the Concomitant Rank-Order Statistics
“Accurate Approximation to the Extreme Order Statistics of Gaussian Samples”, Chen & Tyler 1999
Accurate approximation to the extreme order statistics of Gaussian samples
“Research, Patenting, and Technological Change”, Kortum 1997
“Seeing The Forest From The Trees: When Predicting The Behavior Or Status Of Groups, Correlate Means”, Lubinski & Humphreys 1996b
Seeing The Forest From The Trees: When Predicting The Behavior Or Status Of Groups, Correlate Means
“The Relevance of Group Membership for Personnel Selection: A Demonstration Using Bayes’ Theorem”, Miller 1994
The Relevance of Group Membership for Personnel Selection: A Demonstration Using Bayes’ Theorem
“Validity of the GRE without Restriction of Range”, Huitema & Stein 1993
“Fairness in Employment Testing: Validity Generalization, Minority Issues, and the General Aptitude Test Battery”, Hartigan & Wigdor 1989
“Maxima of Normal Random Vectors: Between Independence and Complete Dependence”, Hüsler & Reiss 1989
Maxima of normal random vectors: Between independence and complete dependence:
View PDF:
“Forecasting Records by Maximum Likelihood”, Smith 1988
“The Asymptotic Theory of Extreme Order Statistics, Second Edition”, Galambos 1987
The Asymptotic Theory of Extreme Order Statistics, Second Edition
“An Examination of Two Alternative Techniques to Estimate the Standard Deviation of Job Performance in Dollars”, Reilly & Smither 1985
“Expected Normal Order Statistics (Exact and Approximate)”, Royston 1982
Expected Normal Order Statistics (Exact and Approximate):
View PDF:
“Impact of Valid Selection Procedures on Work-Force Productivity”, Schmidt et al 1979
Impact of valid selection procedures on work-force productivity
“How Deviant Can You Be?”, Samuelson 1968
“Asymptotic Independence of Certain Statistics Connected With the Extreme Order Statistics in a Bivariate Distribution”, Srivastava 1967
“Estimating Bounds on Athletic Performance”, Deakin 1967
“Asymptotic Independence of Bivariate Extremes”, Mardia 1964
“Expected Values of Normal Order Statistics”, Harter 1961
Expected Values of Normal Order Statistics:
View PDF:
“Bivariate Extreme Statistics, I”, Sibuya 1960
“Statistical Estimates and Transformed Beta-Variables”, Blom 1958
“On the Statistics of Individual Variations of Productivity in Research Laboratories”, Shockley 1957
On the Statistics of Individual Variations of Productivity in Research Laboratories
“The Asymptotical Distribution of Range in Samples from a Normal Population”, Elfving 1947
The Asymptotical Distribution of Range in Samples from a Normal Population
“The Relationship Of Validity Coefficients To The Practical Effectiveness Of Tests In Selection: Discussion And Tables”
“Statistical Method”, Kelley 1923
View PDF (15MB):
“How Many Hottest Days of the Year (So Far)?”
“What Does It Mean to Have a Low R-Squared? A Warning about Misleading Interpretation”
What does it mean to have a low R-squared? A warning about misleading interpretation
“Approximate Order Statistics for Normal Random Variables”
“Univariate Distributional Analysis With L-Moment Statistics Using R”
Univariate Distributional Analysis with L-moment Statistics using R
“Modelling a Time Series of Records With PyMC3”
“Rényi’s Parking Constant”
“Analyzing DeepMind’s Probabilistic Methods for Evaluating Agent Capabilities”
Analyzing DeepMind’s Probabilistic Methods for Evaluating Agent Capabilities:
Wikipedia
Miscellaneous
-
/doc/statistics/order/2022-07-25-gwern-activelearningvsrandomsearch-200simulationruns.webm: -
/doc/statistics/order/2020-11-26-gabrielpeyre-maxgaussianclt.jpg: -
/doc/statistics/order/1996-lubinski-figure1-pilotselection.jpg: -
/doc/statistics/order/gwern-topp-necessarycorrelationstrengthtoreach50percent.jpg: -
/doc/statistics/order/gwern-orderstatistics-selection-multivssingle.jpg: -
/doc/statistics/order/gwern-orderstatistics-selection-bivariate-negativecorrelation.png: -
/doc/statistics/order/gwern-orderstatistics-multistageselection-n48.jpg: -
/doc/statistics/order/gwern-orderstatistics-increasedvarianceadvantage.png: -
/doc/statistics/order/gwern-orderstatistics-increasedvarianceadvantage-n10000.png: -
/doc/statistics/order/gwern-orderstatistics-increasedvarianceadvantage-n1000.png: -
/doc/statistics/order/gwern-orderstatistics-increasedvarianceadvantage-n100.png: -
https://brooker.co.za/blog/2018/01/01/balls-into-bins.html: -
https://www.johndcook.com/blog/2023/05/30/reviewing-a-thousand-things/:View External Link:
https://www.johndcook.com/blog/2023/05/30/reviewing-a-thousand-things/ -
https://www.johndcook.com/blog/2023/06/09/coupon-collector-2/:View External Link:
https://www.johndcook.com/blog/2023/06/09/coupon-collector-2/ -
https://www.johndcook.com/blog/2023/09/30/consecutive-coupon-collector-problem/:View External Link:
https://www.johndcook.com/blog/2023/09/30/consecutive-coupon-collector-problem/ -
https://www.lesswrong.com/posts/EbFABnst8LsidYs5Y/goodhart-taxonomy -
https://www.quantamagazine.org/computer-scientists-invent-an-efficient-new-way-to-count-20240516/ -
https://www.science.org/content/blog-post/target-based-drug-discovery-waste-time
Bibliography
-
2023-sadri.pdf: “Is Target-Based Drug Discovery Efficient? Discovery and ‘Off-Target’ Mechanisms of All Drugs”, -
https://arxiv.org/abs/2210.10760#openai: “Scaling Laws for Reward Model Overoptimization”, -
https://www.sciencedirect.com/science/article/pii/S1359644620305274#sec0010: “Artificial Intelligence in Drug Discovery: What Is Realistic, What Are Illusions? Part 1: Ways to Make an Impact, and Why We Are Not There Yet: Quality Is More Important Than Speed and Cost in Drug Discovery”, -
https://www.nber.org/system/files/working_papers/w28340/w28340.pdf: “Recipes and Economic Growth: A Combinatorial March Down an Exponential Tail”, -
2020-chatterjee.pdf: “A New Coefficient of Correlation”, -
2017-spain.pdf: “Is Individual Job Performance Distributed According to a Power Law? A Review of Methods for Comparing Heavy-Tailed Distributions”, -
https://www.lesswrong.com/posts/dC7mP5nSwvpL65Qu5/why-the-tails-come-apart: “Why the Tails Come Apart”, -
2012-oboyle.pdf: “The Best And The Rest: Revisiting The Norm Of Normality Of Individual Performance”, -
1997-kortoum.pdf: “Research, Patenting, and Technological Change”, -
1996-lubinski-2.pdf: “Seeing The Forest From The Trees: When Predicting The Behavior Or Status Of Groups, Correlate Means”, -
1994-miller.pdf: “The Relevance of Group Membership for Personnel Selection: A Demonstration Using Bayes’ Theorem”, -
1964-mardia.pdf: “Asymptotic Independence of Bivariate Extremes”,