- See Also
- Gwern
-
Links
- “Towards a Law of Iterated Expectations for Heuristic Estimators”, Christiano et al 2024
- “Statistical Patterns in the Equations of Physics and the Emergence of a Meta-Law of Nature”, Constantin et al 2024
- “A Proof That HT Is More Likely to Outnumber HH Than vice Versa in a Sequence of n Coin Flips”, Segert 2024
- “How to Answer Questions of the Type: If You Toss a Coin n Times, How Likely Is HH to Show up More Than HT?”, Ekhad & Zeilberger 2024
- “Verified Neural Compressed Sensing”, Bunel et al 2024
- “Impossible Hypotheses and Effect-Size Limits”, Tilburg & Tilburg 2023
- “Fair Coins Tend to Land on the Same Side They Started: Evidence from 350,757 Flips”, Bartoš et al 2023
- “How Correlated Are You?”, Downey 2023
- “The Lindy Effect”, Ord 2023
- “Sciama’s Argument on Life in a Random Universe: Distinguishing Apples from Oranges”, Wang & Braunstein 2023
- “Distinct Elements in Streams: An Algorithm for the (Text) Book”, Chakraborty et al 2023
- “Arithmetic Sampling: Parallel Diverse Decoding for Large Language Models”, Vilnis et al 2022
- “Why Are Roman-Period Dice Asymmetrical? An Experimental and Quantitative Approach”, Eerkens & Voogt 2022
- “Policy Learning and Evaluation With Randomized Quasi-Monte Carlo”, Arnold et al 2022
- “A High-Dimensional Sphere Spilling out of a High-Dimensional Cube despite Exponentially Many Constraints”, Fort 2022
- “Learning in High Dimension Always Amounts to Extrapolation”, Balestriero et al 2021
- “Can Humans Perform Mental Regression on a Graph? Accuracy and Bias in the Perception of Scatterplots”, Ciccione & Dehaene 2021
- “The Piranha Problem: Large Effects Swimming in a Small Pond”, Tosh et al 2021
- “A New Coefficient of Correlation”, Chatterjee 2020
- “Monte Carlo Gradient Estimation in Machine Learning”, Mohamed et al 2019
- “Going Critical”, Simler 2019
- “Follow-Up: I Found Two Identical Packs of Skittles, among 468 Packs With a Total of 27,740 Skittles”, Farmer 2019
- “Scale-Free Networks Are Rare”, Broido & Clauset 2019
- “Finite Mixture Models”, McLachlan et al 2019
- “Statistical Aspects of Wasserstein Distances”, Panaretos & Zemel 2019
- “Test Driving ‘Power of Two Random Choices’ Load Balancing”, Tarreau 2019
- “Tweedie Gradient Boosting for Extremely Unbalanced Zero-Inflated Data”, Zhou et al 2018
- “How to Shuffle a Big Dataset”, Hardin 2018
- “Logistic Regression Is Not Fucked”, Westfall 2018
- “Information Flow Reveals Prediction Limits in Online Social Activity”, Bagrow et al 2017
- “Requiem for a Shuffle: Why Steve Jobs Told Me He Loved the Littlest IPod—And Why We’re Going to Miss It”, Levy 2017
- “Varieties of Confidence Intervals”, Cousineau 2017
- “Asymptotically Optimal Amplifiers for the Moran Process”, Goldberg et al 2016
- “Amplifiers and Suppressors of Selection for the Moran Process on Undirected Graphs”, Giakkoupis 2016
- “Categorical Reparameterization With Gumbel-Softmax”, Jang et al 2016
- “The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables”, Maddison et al 2016
- “Yule’s ‘Nonsense Correlation’ Solved!”, Ernst et al 2016
- “Amplifiers for the Moran Process”, Galanis et al 2015
- “Practical Probabilistic Programming With Monads”, Ścibior et al 2015
- “Most Undirected Random Graphs Are Amplifiers of Selection for Birth-Death Dynamics, but Suppressors of Selection for Death-Birth Dynamics”, Hindersin & Traulsen 2015
- “What Teachers Should Know about the Bootstrap: Resampling in the Undergraduate Statistics Curriculum”, Hesterberg 2014
- “Red Black Card Game and Generalized Catalan Numbers”, Howe 2014
- “Asymptotic Expression for the Fixation Probability of a Mutant in Star Graphs”, Chalub 2014
- “Universality of Fixation Probabilities in Randomly Structured Populations”, Adlam & Nowak 2014
- “Fixation Probabilities on Superstars, Revisited and Revised”, Jamieson-Lane & Hauert 2013
- “On the Distribution of Job Performance: The Role of Measurement Characteristics in Observed Departures from Normality”, Beck et al 2013
- “Star Performers in 21st Century Organizations”, Aguinis & O’Boyle 2013
- “Stein’s Paradox [Blog]”, Wasserman 2013
- “Page Weight Matters”, Zacharias 2012
- “Indefinite Survival through Backup Copies”, Sandberg & Armstrong 2012
- “Predicting the Outcome of Roulette”, Small & Tse 2012
- “Uniform Random Generation of Large Acyclic Digraphs”, Kuipers & Moffa 2012
- “Counting YouTube Videos via Random Prefix Sampling”, Zhou et al 2011
- “Emergence of Good Conduct, Scaling and Zipf Laws in Human Behavioral Sequences in an Online World”, Thurner et al 2011
- “Quality of Random Number Generators Affects Results of Monte Carlo Simulations for Organic and Biological Systems”, Click et al 2011
- “A New Car-Following Model Yielding Log-Normal Type Headways Distributions”, Li et al 2010
- “Does Your IPod Really Play Favorites?”, Froelich et al 2009
- “When to Stop: How to Gamble If You Must—The Mathematics of Optimal Stopping”, Hill 2009
- “Optimal Stopping of a Brownian Bridge”, Ekström & Wanntorp 2009
- “Weldon’s Dice, Automated”, Labby 2009
- “The Epic Story of Maximum Likelihood”, Stigler 2007
- “Power-Law Distributions in Empirical Data”, Clauset et al 2007
- “The Complex Dynamics of Collaborative Tagging”, Halpin et al 2007
- “An Introduction to the Theory of Citing”, Simkin & Roychowdhury 2007
- “Isaac Newton As a Probabilist”, Stigler 2006
- “Modeling Bursts and Heavy Tails in Human Dynamics”, Vazquez et al 2005
- “Continuous Parameter Estimation Model: Expanding the Standard Statistical Paradigm”, Gorsuch 2005
- “An Alternative to Null-Hypothesis Statistical-Significance Tests”, Killeen 2005
- “Modelling the Recent Common Ancestry of All Living Humans”, Rohde et al 2004
- “Stochastic Modeling of Citation Slips”, Simkin & Roychowdhury 2004
- “Copied Citations Create Renowned Papers?”, Simkin & Roychowdhury 2003
- “Solution to the OK Corral Model via Decoupling of Friedman’s Urn”, Kingman & Volkov 2003
- “Read Before You Cite!”, Simkin & Roychowdhury 2002
- “The Power of Two Random Choices: A Survey of Techniques and Results”, Mitzenmacher et al 2001
- “The Distribution of N-Grams”, Egghe 2000
- “A Primer on Regression Artifacts”, Campbell & Kenny 1999
- “How Many Birds Are There?”, Gaston & Blackburn 1997
- “Another Comment on O'Cinneide”, Mallows 1991
- “The Mean Is within One Standard Deviation of Any Median”, O’Cinneide 1990
- “A Note on Stochastic Dominance and Inequality Measures”, Muliere & Scarsini 1989
- “Methods for Studying Coincidences”, Diaconis & Mosteller 1989
- “Randomness Conservation Inequalities; Information and Independence in Mathematical Theories”, Levin 1984
- “Application of the Buffon Needle Problem and Its Extensions to Parallel-Line Search Sampling Scheme”, Chung 1981 (page 5)
- “A Convergent Gambling Estimate Of The Entropy Of English”, Cover & King 1978
- “Characteristic Statistical Problems of Stochastic Geometry”, Watson 1977 (page 12)
- “Stabilization in Systems: Chreods and Epigenetic Landscapes”, Waddington 1977
- “A Markov Process of Gene Frequency Change in a Geographically Structured Population”, Maruyama 1974
- “Been A Long, Long Time”, Lafferty 1970
- “Estimating the Magnitude of Experimental Effects”, Fleiss 1969
- “How Deviant Can You Be?”, Samuelson 1968
- “A Simple Randomization Procedure”, Sandelius 1962
- “Generation of Random Permutations of Given Number of Elements Using Random Sampling Numbers”, Rao 1961
- “Chance Remarks”, Pierce 1949
- “The Limits of a Measure of Skewness”, Hotelling & Solomons 1932
- “There Is Still Only One Test”, Downey 2024
- “Visualizing Algorithms”
- “Zero Tolerance for Bias”
- “User Probabilityislogic”, probabilityislogic 2024
- “Research Update: Towards a Law of Iterated Expectations for Heuristic Estimators”
- “How Long Does It Take to Become Gaussian?”
- “The Infinitesimal Model: Definition, Derivation, and Implications”
- Wikipedia
- Miscellaneous
- Bibliography
See Also
Gwern
“A World Where the Gambler’s Fallacy Was True via Sampling-Without-Replacement”, Gwern 2024
A world where the gambler’s fallacy was true via Sampling-Without-Replacement
“Calculating The Gaussian Expected Maximum”, Gwern 2016
“Leaky Pipelines”, Gwern 2014
Links
“Towards a Law of Iterated Expectations for Heuristic Estimators”, Christiano et al 2024
Towards a Law of Iterated Expectations for Heuristic Estimators
“Statistical Patterns in the Equations of Physics and the Emergence of a Meta-Law of Nature”, Constantin et al 2024
Statistical Patterns in the Equations of Physics and the Emergence of a Meta-Law of Nature
“A Proof That HT Is More Likely to Outnumber HH Than vice Versa in a Sequence of n Coin Flips”, Segert 2024
A proof that HT is more likely to outnumber HH than vice versa in a sequence of n coin flips
“How to Answer Questions of the Type: If You Toss a Coin n Times, How Likely Is HH to Show up More Than HT?”, Ekhad & Zeilberger 2024
“Verified Neural Compressed Sensing”, Bunel et al 2024
“Impossible Hypotheses and Effect-Size Limits”, Tilburg & Tilburg 2023
“Fair Coins Tend to Land on the Same Side They Started: Evidence from 350,757 Flips”, Bartoš et al 2023
Fair coins tend to land on the same side they started: Evidence from 350,757 Flips
“How Correlated Are You?”, Downey 2023
“The Lindy Effect”, Ord 2023
“Sciama’s Argument on Life in a Random Universe: Distinguishing Apples from Oranges”, Wang & Braunstein 2023
Sciama’s argument on life in a random universe: Distinguishing apples from oranges
“Distinct Elements in Streams: An Algorithm for the (Text) Book”, Chakraborty et al 2023
Distinct Elements in Streams: An Algorithm for the (Text) Book
“Arithmetic Sampling: Parallel Diverse Decoding for Large Language Models”, Vilnis et al 2022
Arithmetic Sampling: Parallel Diverse Decoding for Large Language Models
“Why Are Roman-Period Dice Asymmetrical? An Experimental and Quantitative Approach”, Eerkens & Voogt 2022
Why are Roman-period dice asymmetrical? An experimental and quantitative approach
“Policy Learning and Evaluation With Randomized Quasi-Monte Carlo”, Arnold et al 2022
Policy Learning and Evaluation with Randomized Quasi-Monte Carlo
“A High-Dimensional Sphere Spilling out of a High-Dimensional Cube despite Exponentially Many Constraints”, Fort 2022
“Learning in High Dimension Always Amounts to Extrapolation”, Balestriero et al 2021
“Can Humans Perform Mental Regression on a Graph? Accuracy and Bias in the Perception of Scatterplots”, Ciccione & Dehaene 2021
Can humans perform mental regression on a graph? Accuracy and bias in the perception of scatterplots
“The Piranha Problem: Large Effects Swimming in a Small Pond”, Tosh et al 2021
“A New Coefficient of Correlation”, Chatterjee 2020
“Monte Carlo Gradient Estimation in Machine Learning”, Mohamed et al 2019
“Going Critical”, Simler 2019
“Follow-Up: I Found Two Identical Packs of Skittles, among 468 Packs With a Total of 27,740 Skittles”, Farmer 2019
Follow-up: I found two identical packs of Skittles, among 468 packs with a total of 27,740 Skittles
“Scale-Free Networks Are Rare”, Broido & Clauset 2019
“Finite Mixture Models”, McLachlan et al 2019
“Statistical Aspects of Wasserstein Distances”, Panaretos & Zemel 2019
“Test Driving ‘Power of Two Random Choices’ Load Balancing”, Tarreau 2019
“Tweedie Gradient Boosting for Extremely Unbalanced Zero-Inflated Data”, Zhou et al 2018
Tweedie Gradient Boosting for Extremely Unbalanced Zero-inflated Data
“How to Shuffle a Big Dataset”, Hardin 2018
“Logistic Regression Is Not Fucked”, Westfall 2018
“Information Flow Reveals Prediction Limits in Online Social Activity”, Bagrow et al 2017
Information flow reveals prediction limits in online social activity
“Requiem for a Shuffle: Why Steve Jobs Told Me He Loved the Littlest IPod—And Why We’re Going to Miss It”, Levy 2017
“Varieties of Confidence Intervals”, Cousineau 2017
“Asymptotically Optimal Amplifiers for the Moran Process”, Goldberg et al 2016
“Amplifiers and Suppressors of Selection for the Moran Process on Undirected Graphs”, Giakkoupis 2016
Amplifiers and Suppressors of Selection for the Moran Process on Undirected Graphs
“Categorical Reparameterization With Gumbel-Softmax”, Jang et al 2016
“The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables”, Maddison et al 2016
The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables
“Yule’s ‘Nonsense Correlation’ Solved!”, Ernst et al 2016
“Amplifiers for the Moran Process”, Galanis et al 2015
“Practical Probabilistic Programming With Monads”, Ścibior et al 2015
“Most Undirected Random Graphs Are Amplifiers of Selection for Birth-Death Dynamics, but Suppressors of Selection for Death-Birth Dynamics”, Hindersin & Traulsen 2015
“What Teachers Should Know about the Bootstrap: Resampling in the Undergraduate Statistics Curriculum”, Hesterberg 2014
What Teachers Should Know about the Bootstrap: Resampling in the Undergraduate Statistics Curriculum
“Red Black Card Game and Generalized Catalan Numbers”, Howe 2014
“Asymptotic Expression for the Fixation Probability of a Mutant in Star Graphs”, Chalub 2014
Asymptotic expression for the fixation probability of a mutant in star graphs
“Universality of Fixation Probabilities in Randomly Structured Populations”, Adlam & Nowak 2014
Universality of fixation probabilities in randomly structured populations
“Fixation Probabilities on Superstars, Revisited and Revised”, Jamieson-Lane & Hauert 2013
“On the Distribution of Job Performance: The Role of Measurement Characteristics in Observed Departures from Normality”, Beck et al 2013
“Star Performers in 21st Century Organizations”, Aguinis & O’Boyle 2013
“Stein’s Paradox [Blog]”, Wasserman 2013
“Page Weight Matters”, Zacharias 2012
“Indefinite Survival through Backup Copies”, Sandberg & Armstrong 2012
“Predicting the Outcome of Roulette”, Small & Tse 2012
“Uniform Random Generation of Large Acyclic Digraphs”, Kuipers & Moffa 2012
“Counting YouTube Videos via Random Prefix Sampling”, Zhou et al 2011
“Emergence of Good Conduct, Scaling and Zipf Laws in Human Behavioral Sequences in an Online World”, Thurner et al 2011
Emergence of good conduct, scaling and Zipf laws in human behavioral sequences in an online world
“Quality of Random Number Generators Affects Results of Monte Carlo Simulations for Organic and Biological Systems”, Click et al 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
“Does Your IPod Really Play Favorites?”, Froelich et al 2009
“When to Stop: How to Gamble If You Must—The Mathematics of Optimal Stopping”, Hill 2009
When to Stop: How to gamble if you must—the mathematics of optimal stopping:
View PDF:
“Optimal Stopping of a Brownian Bridge”, Ekström & Wanntorp 2009
“Weldon’s Dice, Automated”, Labby 2009
“The Epic Story of Maximum Likelihood”, Stigler 2007
“Power-Law Distributions in Empirical Data”, Clauset et al 2007
“The Complex Dynamics of Collaborative Tagging”, Halpin et al 2007
“An Introduction to the Theory of Citing”, Simkin & Roychowdhury 2007
“Isaac Newton As a Probabilist”, Stigler 2006
“Modeling Bursts and Heavy Tails in Human Dynamics”, Vazquez et al 2005
“Continuous Parameter Estimation Model: Expanding the Standard Statistical Paradigm”, Gorsuch 2005
Continuous Parameter Estimation Model: Expanding the Standard Statistical Paradigm:
“An Alternative to Null-Hypothesis Statistical-Significance Tests”, Killeen 2005
An alternative to null-hypothesis statistical-significance tests
“Modelling the Recent Common Ancestry of All Living Humans”, Rohde et al 2004
“Stochastic Modeling of Citation Slips”, Simkin & Roychowdhury 2004
“Copied Citations Create Renowned Papers?”, Simkin & Roychowdhury 2003
“Solution to the OK Corral Model via Decoupling of Friedman’s Urn”, Kingman & Volkov 2003
Solution to the OK Corral Model via Decoupling of Friedman’s Urn
“Read Before You Cite!”, Simkin & Roychowdhury 2002
“The Power of Two Random Choices: A Survey of Techniques and Results”, Mitzenmacher et al 2001
The Power of Two Random Choices: A Survey of Techniques and Results
“The Distribution of N-Grams”, Egghe 2000
“A Primer on Regression Artifacts”, Campbell & Kenny 1999
“How Many Birds Are There?”, Gaston & Blackburn 1997
“Another Comment on O'Cinneide”, Mallows 1991
“The Mean Is within One Standard Deviation of Any Median”, O’Cinneide 1990
“A Note on Stochastic Dominance and Inequality Measures”, Muliere & Scarsini 1989
“Methods for Studying Coincidences”, Diaconis & Mosteller 1989
“Randomness Conservation Inequalities; Information and Independence in Mathematical Theories”, Levin 1984
Randomness conservation inequalities; information and independence in mathematical theories
“Application of the Buffon Needle Problem and Its Extensions to Parallel-Line Search Sampling Scheme”, Chung 1981 (page 5)
Application of the Buffon needle problem and its extensions to parallel-line search sampling scheme
“A Convergent Gambling Estimate Of The Entropy Of English”, Cover & King 1978
“Characteristic Statistical Problems of Stochastic Geometry”, Watson 1977 (page 12)
“Stabilization in Systems: Chreods and Epigenetic Landscapes”, Waddington 1977
Stabilization in systems: Chreods and epigenetic landscapes:
“A Markov Process of Gene Frequency Change in a Geographically Structured Population”, Maruyama 1974
A Markov process of gene frequency change in a geographically structured population
“Been A Long, Long Time”, Lafferty 1970
View PDF:
“Estimating the Magnitude of Experimental Effects”, Fleiss 1969
“How Deviant Can You Be?”, Samuelson 1968
“A Simple Randomization Procedure”, Sandelius 1962
“Generation of Random Permutations of Given Number of Elements Using Random Sampling Numbers”, Rao 1961
Generation of Random Permutations of Given Number of Elements Using Random Sampling Numbers
“Chance Remarks”, Pierce 1949
“The Limits of a Measure of Skewness”, Hotelling & Solomons 1932
“There Is Still Only One Test”, Downey 2024
“Visualizing Algorithms”
“Zero Tolerance for Bias”
“User Probabilityislogic”, probabilityislogic 2024
“Research Update: Towards a Law of Iterated Expectations for Heuristic Estimators”
Research update: Towards a Law of Iterated Expectations for Heuristic Estimators
“How Long Does It Take to Become Gaussian?”
“The Infinitesimal Model: Definition, Derivation, and Implications”
The infinitesimal model: Definition, derivation, and implications
Wikipedia
Miscellaneous
-
/doc/statistics/probability/2024-09-05-gwern-meme-butitcouldworkforus-regressiontothemean.jpg: -
/doc/statistics/probability/2018-hardin-shuffle-illustration.png: -
/doc/statistics/probability/2009-ekstrom-figure1-optimalstoppingboundaryofabrownianbridgeproblem.png: -
/doc/statistics/probability/1973-meshalkin-collectionofproblemsinprobabilitytheory.pdf: -
/doc/statistics/probability/1966-feller-anintroductiontoprobabilitytheoryanditsapplications-2.pdf: -
/doc/statistics/probability/1957-feller-anintroductiontoprobabilitytheoryanditsapplications-1.pdf: -
https://aleph.se/andart2/math/weird-probability-distributions/:View External Link:
https://aleph.se/andart2/math/weird-probability-distributions/ -
https://allendowney.blogspot.com/2013/08/are-my-data-normal.html: -
https://blog.demofox.org/2017/05/29/when-random-numbers-are-too-random-low-discrepancy-sequences/: -
https://danielroelfs.com/blog/everything-is-a-linear-model/: -
https://dennybritz.com/posts/probability-monads-from-scratch/: -
https://extremelearning.com.au/unreasonable-effectiveness-of-quasirandom-sequences/: -
https://hackage.haskell.org/package/probability:View External Link:
-
https://hedgehogreview.com/issues/markets-and-the-good/articles/language-machinery -
https://joe-antognini.github.io/machine-learning/steins-paradox: -
https://joshualoftus.com/posts/2020-11-23-least-squares-as-springs/ -
https://lindeloev.github.io/tests-as-linear/:View External Link:
-
https://marckhoury.github.io/blog/counterintuitive-properties-of-high-dimensional-space/: -
https://queue.acm.org/detail.cfm?id=3570937:View External Link:
-
https://royalsocietypublishing.org/doi/10.1098/rspa.2013.0193 -
https://www.johndcook.com/blog/2023/09/29/platonic-solids-and-integration/:View External Link:
https://www.johndcook.com/blog/2023/09/29/platonic-solids-and-integration/ -
https://www.lesswrong.com/posts/no5jDTut5Byjqb4j5/six-and-a-half-intuitions-for-kl-divergence -
https://www.lesswrong.com/posts/pEZoTSCxHY3mfPbHu/catastrophic-goodhart-in-rl-with-kl-penalty -
https://www.lesswrong.com/posts/vfb5Seaaqzk5kzChb/when-is-correlation-transitive:View External Link:
https://www.lesswrong.com/posts/vfb5Seaaqzk5kzChb/when-is-correlation-transitive -
https://www.probabilistic-numerics.org/assets/ProbabilisticNumerics.pdf#page=3 -
https://www.quantamagazine.org/computer-scientists-invent-an-efficient-new-way-to-count-20240516/ -
https://www.reddit.com/r/SampleSize/comments/fr4rnl/results_i_asked_you_to_choose_any_integer_from/: -
https://www.stat.berkeley.edu/~aldous/Real-World/million.html: -
View External Link:
Bibliography
-
https://journals.sagepub.com/doi/full/10.1177/25152459231197605: “Impossible Hypotheses and Effect-Size Limits”, -
https://arxiv.org/abs/2210.15458#google: “Arithmetic Sampling: Parallel Diverse Decoding for Large Language Models”, -
2021-ciccione.pdf: “Can Humans Perform Mental Regression on a Graph? Accuracy and Bias in the Perception of Scatterplots”, -
https://arxiv.org/abs/2105.13445: “The Piranha Problem: Large Effects Swimming in a Small Pond”, -
2020-chatterjee.pdf: “A New Coefficient of Correlation”, -
https://www.wired.com/story/requiem-for-the-ipod-shuffle/: “Requiem for a Shuffle: Why Steve Jobs Told Me He Loved the Littlest IPod—And Why We’re Going to Miss It”, -
2009-froelich.pdf: “Does Your IPod Really Play Favorites?”, -
2009-ekstrom.pdf: “Optimal Stopping of a Brownian Bridge”, -
2007-halpin.pdf: “The Complex Dynamics of Collaborative Tagging”, -
https://arxiv.org/abs/physics/0510117: “Modeling Bursts and Heavy Tails in Human Dynamics”, -
https://www.ic.unicamp.br/~celio/peer2peer/math/mitzenmacher-power-of-two.pdf: “The Power of Two Random Choices: A Survey of Techniques and Results”, -
1932-hotelling.pdf: “The Limits of a Measure of Skewness”,