Prob­a­bil­ity & Statistics

How long does it take to be­come Gaus­sian?

Simp­son’s Paradox

Ap­prox­i­mately Bayesian Rea­son­ing: Knigh­tian Uncer­tainty, Good­hart, and the Look-Else­where Effect

Can we always as­sign, and make sense of, sub­jec­tive prob­a­bil­ities?

Laplace’s rule of succession

Risk and un­cer­tainty: A false di­chotomy?

How much do you be­lieve your re­sults?

Cor­re­spon­dence vi­su­al­iza­tions for differ­ent in­ter­pre­ta­tions of “prob­a­bil­ity”

An Illus­trated Proof of the No Free Lunch Theorem

The Kelly Cri­te­rion in 3D

How to Un­der­stand and Miti­gate Risk

A Bayesian Ag­gre­ga­tion Paradox

The Tails Com­ing Apart As Me­taphor For Life

On martingales

A time-in­var­i­ant ver­sion of Laplace’s rule

Re­port like­li­hood ratios

[Question] What is a prob­a­bil­is­tic phys­i­cal the­ory?

Mes­sage Length

Fermi Estimates

On Fre­quen­tism and Bayesian Dogma

What is Bayesi­anism?

How can one ra­tio­nally have very high or very low prob­a­bil­ities of ex­tinc­tion in a pre-paradig­matic field?

Refer­ences & Re­sources for LessWrong

Pseu­do­ran­dom­ness con­test: prizes, re­sults, and analysis

Calcu­lat­ing Kelly

Rad­i­cal Probabilism

The av­er­age North Korean mathematician

Two Dark Side Statis­tics Papers

[Question] How Often Does ¬Cor­re­la­tion ⇏ ¬Cau­sa­tion?

[Question] What does it mean for an event or ob­ser­va­tion to have prob­a­bil­ity 0 or 1 in Bayesian terms?

Map:Ter­ri­tory::Uncer­tainty::Ran­dom­ness – but that doesn’t mat­ter, value of in­for­ma­tion does.

In­sights from “All of Statis­tics”: Probability

In­sights from “All of Statis­tics”: Statis­ti­cal Inference

Sub­scripts for Probabilities

The Uni­vari­ate Fallacy

Gen­er­al­ized Stat Mech: The Boltz­mann Approach

Hy­poth­e­sis Space Entropy

Book Re­view of 5 Ap­plied Bayesian Statis­tics Books

An In­tu­itive Ex­pla­na­tion of Bayes’s Theorem

Statis­ti­cal mod­els & the ir­rele­vance of rare exceptions

Gen­er­al­ised mod­els: im­perfect mor­phisms and in­for­ma­tional entropy

“How the Gaza Health Ministry Fakes Ca­su­alty Num­bers”

Are Bayesian meth­ods guaran­teed to overfit?

When is cor­re­la­tion tran­si­tive?

Bayesian Net­works Aren’t Ne­c­es­sar­ily Causal

Should cor­re­la­tion co­effi­cients be ex­pressed as an­gles?

The Effec­tive­ness Of Masks is Limited

AXRP Epi­sode 36 - Adam Shai and Paul Riech­ers on Com­pu­ta­tional Mechanics

Aver­age prob­a­bil­ities, not log odds

[Cos­mol­ogy Talks] New Prob­a­bil­ity Ax­ioms Could Fix Cos­mol­ogy’s Mul­ti­verse (Par­tially) - Sylvia Wenmackers

Why the tails come apart

Use Nor­mal Predictions

Trust in Bayes

La­tent Vari­ables and Model Mis-Specification

Con­fi­dence in­ter­vals seem to be rarely use­ful, in and of themselves

Most likely is not likely

Mul­ti­vari­ate es­ti­ma­tion & the Squig­gly language

Ep­silon is not a prob­a­bil­ity, it’s a cop-out

12 in­ter­est­ing things I learned study­ing the dis­cov­ery of na­ture’s laws

[Question] Thoughts on the SPIES Fore­cast­ing Method?

Search­ing for outliers

Refer­ence Classes

The prob­lem/​solu­tion ma­trix: Calcu­lat­ing the prob­a­bil­ity of AI safety “on the back of an en­velope”

The Case for Fre­quen­tism: Why Bayesian Prob­a­bil­ity is Fun­da­men­tally Un­sound and What Science Does Instead

Large Effects Can’t Prove Small Causes

scipy.op­ti­mize.curve_fit Is Awesome

E.T. Jaynes Prob­a­bil­ity The­ory: The logic of Science I

[Question] Why cor­re­la­tion, though?

Book re­view: Pearl’s Book of Why

A But­terfly’s View of Probability

Causal In­fer­ence Se­quence Part 1: Ba­sic Ter­minol­ogy and the As­sump­tions of Causal Inference

Causal In­fer­ence Se­quence Part II: Graph­i­cal Models

“Statis­ti­cal Bias”

“In­duc­tive Bias”

Very Short In­tro­duc­tion to Bayesian Model Com­par­i­son

Six (and a half) in­tu­itions for KL divergence

From Laplace to BIC

Bayesian Model Test­ing Comparisons

Cross-Val­i­da­tion vs Bayesian Model Comparison

Book Re­view—Prob­a­bil­ity and Fi­nance: It’s Only a Game!

Why square er­rors?

“A Defi­ni­tion of Sub­jec­tive Prob­a­bil­ity” by An­scombe and Aumann

Log­i­cal in­duc­tion for soft­ware engineers

Neu­ral un­cer­tainty es­ti­ma­tion re­view ar­ti­cle (for al­ign­ment)

Book Re­view: Fooled by Randomness

[Question] What does “prob­a­bil­ity” re­ally mean?

0 and 1 aren’t probabilities

What makes a prob­a­bil­ity ques­tion “well-defined”? (Part II: Ber­trand’s Para­dox)

Vi­su­al­i­sa­tion of Prob­a­bil­ity Mass

Stan­zas On Power Calculation

Prob­a­bil­ity The­ory: The Logic of Science, Jaynes

Prob­a­bil­ity Space & Au­mann Agreement

“Pre­dic­tion” and “ex­pla­na­tion” are not causation

Au­mann’s Agree­ment Revisited

The Joys of Con­ju­gate Priors

In­for­ma­tion Charts

Pre­ci­sion of Sets of Forecasts

Prob­a­bil­ity, knowl­edge, and meta-probability

Case study: abuse of fre­quen­tist statistics

Bayesi­anism for hu­mans: “prob­a­ble enough”

If It’s Worth Do­ing, It’s Worth Do­ing With Made-Up Statistics

Fo­rum Karma: view stats and find highly-rated com­ments for any LW user

Beyond Bayesi­ans and Frequentists

Yes, Virginia, You Can Be 99.99% (Or More!) Cer­tain That 53 Is Prime

Con­fi­dence lev­els in­side and out­side an argument

Beau­tiful Probability

The cen­tral limit the­o­rem in terms of convolutions

The Se­cond Law of Ther­mo­dy­nam­ics, and Eng­ines of Cognition

Rugby & Re­gres­sion Towards the Mean

[Question] What are prin­ci­pled ways for pe­nal­is­ing com­plex­ity in prac­tice?

Quadratic mod­els and (un)falsified data

How to come up with ver­bal probabilities

Learn­ing as you play: an­thropic shadow in deadly games

Use­ful Statis­ti­cal Biases

What’s wrong with this pic­ture?

Kling, Prob­a­bil­ity, and Economics

Sam­ple means, how do they work?

Fre­quen­tist prac­tice in­cor­po­rates prior in­for­ma­tion all the time

From game the­ory to play­ers theory

[Question] Does there ex­ist a de­tailed Bayesian COVID tracker?

How Not to be Stupid: Adorable Maybes

Log-odds (or log­its)

[Question] Did any­body calcu­late the Bri­ers score for per-state elec­tion fore­casts?

The Fal­lacy of Large Numbers

Free Stats Text­book: Prin­ci­ples of Uncertainty

[Question] Cur­rent State of Prob­a­bil­is­tic Logic

Un­der­speci­fied Prob­a­bil­ities: A Thought Ex­per­i­ment

Prob­a­bil­ity dis­tri­bu­tions and writ­ing style

in­dex­i­cal un­cer­tainty and the Ax­iom of Independence

Con­volu­tion as smoothing

Causal­ity does not im­ply correlation

An el­e­gant proof of Laplace’s rule of succession

The Pre­dic­tion Hierarchy

[Question] In­finite tower of meta-probability

Eliezer’s ex­am­ple on Bayesian statis­tics is wr… oops!

How Less­wrong helped me make $25K: A ra­tio­nal pric­ing strategy

Prob­a­bil­ity vs Likelihood

Are dogs bad?

[Question] What is the se­man­tics of as­sign­ing prob­a­bil­ities to fu­ture events?

The Ja­panese Quiz: a Thought Ex­per­i­ment of Statis­ti­cal Epistemology

a vi­sual ex­pla­na­tion of Bayesian updating

Does but­terfly af­fect?

The Gen­er­al­ized Product Rule

[Question] Is it true that most stud­ies in Kah­ne­man’s ‘Think­ing fast and slow’ are not repli­ca­ble and the book is largely not sup­ported by ev­i­dence?

[Question] Jay­ne­sian in­ter­pre­ta­tion—How does “es­ti­mat­ing prob­a­bil­ities” make sense?

[Question] Do Bayesi­ans like Bayesian model Aver­ag­ing?

[Question] Halpern’s pa­per—A re­fu­ta­tion of Cox’s the­o­rem?

[Question] Jaynes-Cox Prob­a­bil­ity: Are plau­si­bil­ities ob­jec­tive?

[Question] Has Van Horn fixed Cox’s the­o­rem?

[Question] Causal with­out cor­re­la­tion, how?

[Question] Is LessWrong dead with­out Cox’s the­o­rem?

Book Re­view: The End of Average

Poker with Lennier

[Question] Does any­one know what Marvin Min­sky is talk­ing about here?

Find­ing the Cen­tral Limit The­o­rem in Bayes’ rule

Com­mon Prob­a­bil­ity Distributions

A Gen­er­al­iza­tion of ROC AUC for Bi­nary Classifiers

Anti-cor­re­lated causation

Some thoughts about an es­ti­ma­tor by Taleb

Tar­get for Tonight: A Drama In One Act

Ret­ro­spec­tive forecasting

A com­pila­tion of mi­suses of statistics

Prac­ti­cal use of the Beta dis­tri­bu­tion for data analysis

Don’t be afraid of the thou­sand-year-old vampire

De­con­fus­ing Lan­dauer’s Principle

[Question] What is the most prob­a­ble AI?

Five views of Bayes’ Theorem

Utility func­tions and prob­a­bil­ities are entangled

Statis­tics for vague con­cepts and “Colors” of places

Statis­tics for ob­jects with shared identities

The high­est-prob­a­bil­ity out­come can be out of distribution

[Question] Why are prob­a­bil­ities rep­re­sented as real num­bers in­stead of ra­tio­nal num­bers?

Mir­a­cles and why not to be­lieve them

Re­view: Bayesian Statis­tics the Fun Way by Will Kurt

Why Bet Kelly?

A hun­dredth of a bit of ex­tra entropy

The AI Con­trol Prob­lem in a wider in­tel­lec­tual context

The Best Text­books on Every Subject

The me­dian and mode use less in­for­ma­tion than the mean does

Reflect­ing on the tran­shu­man­ist re­but­tal to AI ex­is­ten­tial risk and cri­tique of our de­bate method­olo­gies and mi­suse of statistics

The Solu­tion to Sleep­ing Beauty

Pre­dict­ing AGI by the Tur­ing Test

[Question] What is an ap­pro­pri­ate sam­ple size when sur­vey­ing billions of data points?

“Gen­langs” and Zipf’s Law: Do lan­guages gen­er­ated by ChatGPT statis­ti­cally look hu­man?

The Ap Distribution

[Question] Are (Mo­tor)sports like F1 a good thing to cal­ibrate es­ti­mates against?

Math-to-English Cheat Sheet

Out-of-body rea­son­ing (OOBR)

Prob­a­bly Not a Ghost Story

″… than av­er­age” is (al­most) meaningless

[Question] Cal­ibra­tion train­ing for ‘per­centile rank­ings’?

Con­fus­ing the met­ric for the mean­ing: Per­haps cor­re­lated at­tributes are “nat­u­ral”

In­ten­tion-to-Treat (Re: How harm­ful is mu­sic, re­ally?)

How long should poli­ti­cal (and other) terms be?

“It’s a 10% chance which I did 10 times, so it should be 100%”

De­bunked And Well-Refuted

Mak­ing bet­ter es­ti­mates with scarce information

[Question] Where to start with statis­tics if I want to mea­sure things?

Aver­ages and sam­ple sizes

Quan­topian con­test, but for food in­take and weight

Aver­ag­ing sam­ples from a pop­u­la­tion with log-nor­mal distribution

A con­cep­tual pre­cur­sor to to­day’s lan­guage ma­chines [Shan­non]

[Linkpost] Re­marks on the Con­ver­gence in Distri­bu­tion of Ran­dom Neu­ral Net­works to Gaus­sian Pro­cesses in the In­finite Width Limit

Born as the sev­enth month dies …

Shut Up And Guess

If a tree falls on Sleep­ing Beauty...

“No ev­i­dence” as a Valley of Bad Rationality

Why We Can’t Take Ex­pected Value Es­ti­mates Liter­ally (Even When They’re Un­bi­ased)

Co-Proofs

A Proper Scor­ing Rule for Con­fi­dence Intervals

Me­taMed: Ev­i­dence-Based Healthcare

Even if you have a nail, not all ham­mers are the same

Rea­son­able Explanations

Tech­niques for prob­a­bil­ity estimates

Punc­tu­al­ity—Ar­riv­ing on Time and Math

Prob­a­bil­ity space has 2 metrics

Fre­quen­tist Statis­tics are Fre­quently Subjective

Ex­ces­sive EDA Effortposting

Reflec­tion in Prob­a­bil­is­tic Logic

His­tory of LessWrong: Some Data Graphics

A Mo­tor­cy­cle (and Cal­ibra­tion?) Accident

Against NHST

Anti-akra­sia tool: like stickK.com for data nerds

New Im­proved Lottery

Gears vs Behavior

In­ter­pre­ta­tions of “prob­a­bil­ity”

What would con­vince you you’d won the lot­tery?

Cir­cu­lar Altruism

0 And 1 Are Not Probabilities

A Fer­vent Defense of Fre­quen­tist Statistics

Fun­nel plots: the study that didn’t bark, or, vi­su­al­iz­ing re­gres­sion to the null

Lot­ter­ies: A Waste of Hope

Con­founded No Longer: In­sights from ‘All of Statis­tics’

Effect het­ero­gene­ity and ex­ter­nal val­idity in medicine

Fre­quen­tist Magic vs. Bayesian Magic

Noisy Poll Re­sults And Rep­tilian Mus­lim Cli­ma­tol­o­gists from Mars

Diseased dis­ci­plines: the strange case of the in­verted chart

Multiplicitous

Wolf’s Dice II: What Asym­me­try?

Wolf’s Dice

Chart­ing Deaths: Real­ity vs Reported

The Pyra­mid And The Garden

The Statis­ti­cian’s Fallacy

DSLT 1. The RLCT Mea­sures the Effec­tive Di­men­sion of Neu­ral Networks

Us­ing de­grees of free­dom to change the past for fun and profit

In­stinc­tive Fre­quen­tists, the Out­side View, and de-Biasing

Hu­man perfor­mance, psy­chom­e­try, and base­ball statistics

No non­sense ver­sion of the “racial al­gorithm bias”

A Pois­son pro­cess paradox

Bayes’ The­o­rem in three pictures

Crypto quant trad­ing: Intro

Crypto quant trad­ing: Naive Bayes

 How Should We Cri­tique Re­search? A De­ci­sion Perspective

Sub­text is not in­var­i­ant un­der lin­ear transformations

What Are Prob­a­bil­ities, Any­way?

Prob­a­bil­ity in­ter­pre­ta­tions: Examples

Prob­a­bil­ity is Sub­jec­tively Objective

Pri­ors as Math­e­mat­i­cal Objects

Hor­rible LHC Inconsistency

Imag­ine a World Where Govern­ments Treated COVID-19 Properly

Bayesian Flame

[Link] “Fewer than X% of Amer­i­cans know Y”

Coun­ter­fac­tual out­come state tran­si­tion parameters

When (Not) To Use Probabilities

Com­plex­ity Penalties in Statis­ti­cal Learning

Re­quire­ments for a STEM-ca­pa­ble AGI Value Learner (my Case for Less Doom)

Rais­ing the fore­cast­ing wa­ter­line (part 1)

DSLT 2. Why Neu­ral Net­works obey Oc­cam’s Razor

DSLT 4. Phase Tran­si­tions in Neu­ral Networks

DSLT 3. Neu­ral Net­works are Singular

Co­var­i­ance in your sam­ple vs co­var­i­ance in the gen­eral population

Ad­ven­tist Health Study-2 sup­ports pesc­etar­i­anism more than veganism

Mov­ing to a World Beyond “p < 0.05”

DSLT 0. Distill­ing Sin­gu­lar Learn­ing Theory

The dan­gers of zero and one

How sub­jec­tive is at­trac­tive­ness?

Vi­su­al­iz­ing the power of mul­ti­ple step se­lec­tion pro­cesses in JS: Gal­ton’s bean machine

(Sub­jec­tive Bayesi­anism vs. Fre­quen­tism) VS. For­mal­ism

Laplace Approximation

VC The­ory Overview

The In­spec­tion Para­dox is Everywhere

In­spec­tion Para­dox as a Driver of Group Separation

In­her­ited Im­prob­a­bil­ities: Trans­fer­ring the Bur­den of Proof

On the Im­por­tance of Sys­tem­atic Bi­ases in Science

Monty Hall in the Wild

Us­ing ma­chine learn­ing to pre­dict ro­man­tic com­pat­i­bil­ity: em­piri­cal results

[Question] Are there any good, easy-to-un­der­stand ex­am­ples of cases where statis­ti­cal causal net­work dis­cov­ery worked well in prac­tice?

Too good to be true

[Draft] Poker With Lennier