Subject
106 entries
Statistics
Bookmarks
Seeing Theory: visual probability and statistics
Seeing Theory is an interactive visualization project from Brown University that teaches probability and statistics through simulation rather than equations. Six chapters covering basic probability through Bayesian inference, all with manipulable parameters and live experiment feedback.
Stochastic Processes and Simulations: An ML Perspective
Stochastic Processes and Simulations: A Machine Learning Perspective by Vincent Granville — covers point processes, Poisson-binomial processes, GPU clustering, and extreme value theory with Python code. Bridges probability theory and ML's simulation-heavy approach to uncertainty.
R2D3: Visual Introduction to Machine Learning
R2D3 is a visual introduction to machine learning and statistics — scrollytelling essays that use animated D3.js visualizations to explain concepts like decision trees, bias-variance tradeoff, and model comparison. One of the best examples of the genre.
What Are the Most Important Statistical Ideas of the Past 50 Years?
Andrew Gelman and Aki Vehtari's 2021 JASA paper enumerating 8 ideas that most changed statistics in the past 50 years — from counterfactual causal inference to bootstrapping to overparameterized models. A rare high-level synthesis by two of the field's most credible voices.
Regression and Other Stories
Regression and Other Stories by Gelman, Hill, and Vehtari is a practical statistics textbook covering regression modeling from basics through causal inference — grounded in real data examples and the Bayesian workflow. The modern standard for applied regression.
Introduction to Probability for Data Science
Introduction to Probability for Data Science by Stanley Chan is a free undergraduate textbook covering probability theory through regression and hypothesis testing, with code examples in Python, R, MATLAB, and Julia. Designed specifically for the data science curriculum rather than pure math.
An Introduction to Statistical Learning (2nd Edition)
The second edition of James, Witten, Hastie, and Tibshirani's canonical intro-level statistical learning textbook, updated in 2021 to include deep learning, survival analysis, and multiple testing. It sits between undergraduate statistics and the more demanding Elements of Statistical Learning — the best entry point for practitioners who want rigorous but accessible ML foundations.
Peter Norvig's Probability Notebook
Peter Norvig's probability notebook from pytudes — a Jupyter walkthrough of probability theory using clean Python, demonstrating how to simulate and compute probabilities with elegant code. Companion to his broader skill-building notebook collection.
Practical Advice for Analysis of Large, Complex Data Sets
Patrick Riley's practical guide to analyzing large, complex datasets from his years leading data science on Google Search logs. Covers sanity checks, stratification, and pitfalls that statistical theory alone won't protect you from.
Ergodicity: What's It Mean
Avoid Boring People's explainer on ergodicity — the distinction between time-average outcomes and ensemble-average outcomes. Core to Ole Peters's critique of expected utility theory and why average returns can be misleading for individual decision-making.
Many Models Workflows in Python
Alex Hayes's port of the R 'many models' workflow pattern to Python — fitting many models across groups using tidy data conventions. Bridges the gap between R's purrr/broom/tidymodels idioms and Python's pandas/scikit-learn ecosystem.
Probabilistic Machine Learning: An Introduction (Murphy)
Kevin Murphy's Probabilistic Machine Learning: An Introduction is the modern update to his 2012 ML textbook — free online, covering everything from linear models through deep learning with a probabilistic framing. The definitive graduate-level ML reference for 2022 onward.
Statistics Revisited
A beginner-friendly revisit of descriptive and inferential statistics for data scientists — covering the Central Limit Theorem, confidence intervals, z-scores, and t-distributions with accessible explanations. Good refresher on the probabilistic foundations underlying most ML evaluation.
Multi-Armed Bandits and the Stitch Fix Experimentation Platform
Stitch Fix's blog on multi-armed bandits as an alternative to A/B testing — Thompson Sampling routes traffic toward better-performing arms dynamically, reducing wasted exposure. Strong motivation for when bandits beat traditional experimentation.
Best Data Science Books According to the Experts
Built In's curated list of best data science books by category, with expert commentary on what each covers and who it's for. Spans introductory statistics through advanced ML, with a practical rather than academic bias.
PRML: Pattern Recognition and Machine Learning Algorithms in Python
Python implementations of algorithms from Bishop's 'Pattern Recognition and Machine Learning' — the canonical probabilistic ML textbook. Bridges the gap between the math in the book and working code.
HN: 40 Statistics Interview Problems and Answers
A Hacker News thread discussing a list of 40 statistics interview problems — the HN comments add context, caveats, and additional problems to the original post. A snapshot of what statistics knowledge is actually tested in data science interviews.
160 Data Science Interview Questions
Alexey Grigorev's compilation of 160 data science interview questions across statistics, machine learning, SQL, and programming — a broad coverage reference for data science interview preparation, organized by topic.
Zipf's Law Arises Naturally When There Are Underlying, Unobserved Variables
A PLOS Computational Biology paper arguing that Zipf's Law — the power law governing word frequency, city size, income distribution, and countless other phenomena — arises naturally whenever observed variables are log-linear functions of hidden unobserved variables. Explains the law's ubiquity without requiring any special generative mechanism.
Why I'm Not a Fan of R-Squared
John Myles White's argument that R-squared is a misleading metric for regression model quality — it conflates the variance of x with model fit and can be gamed. A clean critique that every data scientist who uses linear regression should read.
One Year as a Data Scientist at Stack Overflow
David Robinson's retrospective on his first year as a data scientist at Stack Overflow — what he learned, where the role differed from academic statistics, and why communication matters more than algorithms. A grounded career reflection that aged well.
A Multi-Level Bayesian Analysis of Racial Bias in Police Shootings
A PLOS ONE paper applying multi-level Bayesian hierarchical models to police shooting data across US counties from 2011–2014, finding significant racial disparities in lethal force use. Notable for applying rigorous statistical methods to a politically charged dataset.
The Theorem Every Data Scientist Should Know
Jean-Nicholas Hould's explainer on the Central Limit Theorem as the foundational theorem every data scientist needs to internalize — why sample means approach normality, and why this underpins most of frequentist hypothesis testing and confidence intervals.
The ROC Curve Explained
A visual explanation of the Receiver Operating Characteristic (ROC) curve and AUC for binary classifier evaluation. One of the clearest introductions to the concept for practitioners learning to assess model performance beyond accuracy.
Surfing Silver: Dynamic Bayesian Forecasting for Fun and Profit
Slides from a Data Popup talk on dynamic Bayesian forecasting — applying Bayesian state-space models to time series prediction with uncertainty quantification. One of the cleaner practitioner introductions to Bayesian time series methods from the mid-2010s data science speaker circuit.
Markov Chains Explained Visually
Setosa.io's interactive visual explainer for Markov chains — manipulable transition matrices, live state diagrams, and steady-state convergence demonstrated in browser. The best introductory treatment of the concept available on the web.
Understanding Bayes: How to Become a Bayesian in Eight Easy Steps
Alexander Etz's eight-step guide to adopting Bayesian thinking in statistics — covers prior selection, Bayes factors, and the core philosophical shift from frequentist null-hypothesis testing. A practical on-ramp for scientists trained in classical statistics.
The Three Cultures of Machine Learning
Jason Eisner's JHU tutorial describing three distinct cultures within machine learning — the statistical/probabilistic, the algorithmic/computational, and the geometric/optimization traditions. Useful framing for understanding why ML researchers sometimes talk past each other.
Overfitting, Regularization, and Hyperparameters
DS Walter's practitioner explainer on overfitting, regularization techniques, and hyperparameter tuning — covering L1/L2 penalties, dropout, and cross-validation. A clear introduction to the bias-variance tradeoff for working data scientists.
The Zipf Mystery
A video exploring the mystery of Zipf's Law — why word frequencies, city populations, income distributions, and dozens of other natural and social phenomena follow the same power-law distribution. Directly relevant to the naming of Zipfian Academy.
50 Years of Data Science
David Donoho's essay arguing that 'data science' is a real intellectual discipline distinct from statistics — tracing 50 years of statistical evolution toward greater empiricism, computation, and scale. A foundational text for anyone who wants to understand what data science actually is and where it came from.
How a Kalman Filter Works, in Pictures
The clearest visual explanation of how a Kalman filter works — building from Gaussian distributions to the prediction-update cycle without losing the intuition in the math. A reference that makes the algorithm genuinely understandable rather than just computable.
10 Types of Regressions. Which One to Use?
A reference guide to 10 regression types and when to use each — covering linear, logistic, ridge, lasso, polynomial, and more. The kind of practical decision map that was useful before sklearn docs became as thorough as they are now.
Probable Points and Credible Intervals: Bayesian Decision Theory
Part 2 of Rasmus Baath's gentle intro to Bayesian decision theory — covering how credible intervals and probable points are used to make decisions under uncertainty. One of the cleaner elementary treatments of the Bayesian decision framework.
Introducing Practical and Robust Anomaly Detection in a Time Series
Twitter's 2015 release of AnomalyDetection — an open-source R library using STL decomposition and the Generalized ESD test to find anomalies in time series. One of the first production-grade anomaly detection tools to be open-sourced by a major tech company.
Data Scientist Interview Puzzle Questions — Mike Tamir
Mike Tamir's Quora answer on brainstorming and puzzle questions asked in data science interviews. Useful for both candidates prepping for interviews and hiring managers designing them — the best puzzles test statistical intuition, not memorization.
Statistical Inference for Everyone
Statistical Inference for Everyone (SIE) is a free introductory statistics textbook by Brian Blais that teaches through examples and probability rather than formulas. Recommended as a gentler alternative to frequentist-heavy introductory texts.
Seaborn — Plotting Distributions Notebook
Seaborn's official distribution-plotting example notebook — demonstrates the library's statistical visualization API for histograms, KDE plots, rug plots, and joint distributions. The reference for anyone learning to visualize data distributions in Python.
Lea — Discrete Probability Distributions in Python
Lea is a Python library for working with discrete probability distributions symbolically — defining distributions, computing joint and conditional probabilities, and simulating outcomes. An unusual tool that treats probability as a first-class programming construct.
Introduction to Principal Component Analysis (PCA)
Laura Diane Hamilton's accessible introduction to Principal Component Analysis — covering the geometric and algebraic intuition without requiring a linear algebra background. One of the cleaner beginner explanations of a technique that's notoriously hard to explain well.
Calibrating Classifier Probabilities
Daniel Nee's post on calibrating classifier output probabilities — the underappreciated problem that a model's predicted probability of 0.8 doesn't always mean there's an 80% chance of the positive class. Essential reading before using model outputs for decision-making.
Pykov — Finite Markov Chains in Python
Pykov is a small Python library for working with finite regular Markov chains — define chains from scratch or load from files, compute stationary distributions, simulate walks, and analyze steady-state behavior. Useful for any system that can be modeled as probabilistic state transitions.
How Optimizely (Almost) Got Me Fired
SumAll's account of how Optimizely's 'optional stopping' in A/B tests produced false positives that led to bad product decisions — a landmark post in the backlash against naive A/B testing tools. The core issue: peeking at results and stopping when p<0.05 inflates false positive rates dramatically.
Scalable A/B Experiments at Pinterest
Pinterest's engineering blog on how they built scalable A/B testing infrastructure — covering experiment assignment, metric computation, and statistical significance at Pinterest's scale. A practitioner's account of the gap between textbook A/B testing and production experimentation.
Multiple A/B/n Tests in Marketing with ANOVA and R
Marketing Distillery's practical guide to running multiple A/B/n tests using ANOVA in R — extending the standard two-group t-test to handle multiple variants simultaneously without inflating false positive rates.
Markov Chains Explained Visually
Victor Powell's interactive visual explanation of Markov chains using animated state diagrams — one of the best-known examples of explorable explanations in mathematics. Essential reading for anyone building intuition for probabilistic state systems before tackling HMMs, PageRank, or reinforcement learning.
Pattern Classification Data Glossary
Sebastian Raschka's data science and machine learning glossary from his pattern_classification GitHub repo — a community reference that grew into one of the most-linked ML terminology resources on GitHub. Useful for grounding conversations in shared vocabulary.
Fun with Stats: How Big of a Sample Size Do I Need?
Julia Evans walks through sample size calculation for experiments, grounding statistical power and significance in a concrete worked example. A good entry point for engineers who run A/B tests but haven't internalized what sample size actually buys you.
So You Think You Can Test?
An interactive tool by Lukas Vermeer that lets you distinguish A/A tests from A/B tests visually — a demonstration that human intuition about statistical significance is unreliable. Forces the realization that we can't eyeball whether a difference is real.
Law of Large Numbers and Central Limit Theorem
Bugra Akyildiz's notes on the law of large numbers and the central limit theorem with Python demonstrations — two of the most important foundational theorems in statistics that together explain why averages are well-behaved and why the normal distribution appears everywhere.
Must Read Before Attending Any Data Science Interview
Data Science Central's pre-interview reading list covering statistics, machine learning, coding, and business acumen questions asked in 2014 data science interviews. A historical snapshot of what the field considered core practitioner knowledge.
Bayesian Regression with PyMC: A Brief Tutorial
A Zipfian Academy student's tutorial on Bayesian linear regression using PyMC — notable both as an accessible introduction to probabilistic modeling and as a window into the Zipfian cohort's learning culture of public writing. PyMC was the dominant Python tool for Bayesian modeling at the time.
Zipfian Academy: Week 2 — Or: "A Frequentist and a Bayesian Walk into a Bar..."
A Zipfian Academy student's week 2 post, titled 'A Frequentist and a Bayesian Walk into a Bar' — covering the pivotal statistics week where bootcamp students confronted the philosophical divide between frequentist and Bayesian approaches. One of the most memorable weeks in the curriculum.
20 Short Tutorials All Data Scientists Should Read and Practice
Data Science Central's curated list of 20 short tutorials spanning statistics, machine learning, SQL, R, and Python — designed as quick-read practice exercises. A community-sourced map of what foundational skills were considered essential for data scientists in 2014.
Univariate Distribution Relationship Chart
Lawrence Leemis's interactive chart showing the relationships between 76 univariate probability distributions — which distributions are special cases of others, how they connect via limits and parameter settings. An essential reference chart for anyone working seriously with probability distributions.
Spurious Correlations
Tyler Vigen's Spurious Correlations site generates charts showing absurd correlations between unrelated variables — US cheese consumption vs. deaths by bedsheet tangling, etc. The clearest possible demonstration that correlation does not imply causation.
Zipfian npm Package — Zipf Distribution Generator for Node.js
An npm package for generating Zipf-distributed random numbers in Node.js — useful for modeling rank-frequency phenomena like word counts, city sizes, and website traffic. A small utility from Will Scott born out of a paper deadline.
Programmatically Understanding the Expectation Maximization Algorithm
Nipun Batra's programmatic walkthrough of the Expectation Maximization algorithm — showing the E and M steps in code to build intuition for how EM converges. Makes the algorithm's alternating optimization structure tangible.
Togaware: One Page R — A Survival Guide to Data Science with R
Togaware's One Page R is a survival guide to data science with R — a dense, practical reference document covering the R ecosystem from data loading to modeling to visualization. The 'one page' is ironic; it's comprehensive.
Finding a Zipf Distribution in a Personal Project
Tweet from a Zipfian Academy student (@adailyventure) who found a Zipf distribution in their personal project and asked Ryan Orban if that earned extra credit. A charming moment of applied statistics discovery.
"In God We Trust, All Others Bring Data"
Ryan Orban tweet of reading Hastie's Elements of Statistical Learning with the quote 'In God we trust, all others bring data.' A snapshot of the self-directed study that accompanied the Zipfian Academy period.
Frequentism and Bayesianism: A Practical Introduction
Jake VanderPlas's Python-driven comparison of frequentist and Bayesian statistics — showing the two philosophies side-by-side with code. The most-cited accessible treatment of a distinction that confuses most practitioners.
Statistical Data Mining Tutorials — AutonLab (CMU)
Carnegie Mellon's AutonLab tutorial series on statistical data mining — covering Bayesian networks, clustering, density estimation, dimensionality reduction, and anomaly detection. A rigorous academic reference that was freely available online before MOOC culture normalized that.
How To Choose The Right Test Options When Evaluating Machine Learning Algorithms
Jason Brownlee's guide to choosing between hold-out validation, k-fold cross-validation, and bootstrap estimation when evaluating ML algorithms. Covers when each approach is appropriate given dataset size and computational budget.
German Tank Problem
The German tank problem: WWII Allies estimated German tank production by applying statistical estimation to captured tank serial numbers. A compelling historical case study in the power of statistical inference over conventional intelligence methods.
The Bell Curve Scar — Handicapping Passengers on the Unsinkable Ship
A statistical analysis of Titanic passenger survival rates examining how aggregated bell curve thinking obscures survival disparities by class, gender, and ticket price. Uses Titanic as a historical dataset to illustrate how summary statistics can mislead.
A/B Test Calculator — ABBA (Thumbtack)
Thumbtack's ABBA (A/B Analysis) tool — a Bayesian A/B test calculator that reports the probability one variant beats another, rather than traditional p-values. Practically more useful than frequentist tests for the decisions product teams actually make.
Setosa.io: Conditional Probability Visualizer
Victor Powell's interactive visual explanation of conditional probability — part of the setosa.io series that made abstract statistical concepts tangible through browser-based animation. One of the best examples of explanatory visualization for statistics education.
Optimism in the Face of Uncertainty: the UCB1 Algorithm
Jeremy Kun's accessible treatment of the UCB1 algorithm — the principle of 'optimism in the face of uncertainty' formalized as a bandit algorithm with proven regret bounds. Shows why adding a confidence bonus to estimated rewards elegantly solves the exploration-exploitation tradeoff.
Optimal Thompson Sampling: Asymptotic Analysis
Emilie Kaufmann's arXiv paper on the asymptotic optimality of Thompson Sampling for multi-armed bandits — the theoretical grounding that explains why Thompson Sampling works as well as it does empirically. Proves it achieves near-optimal regret bounds.
Multi-Armed Bandits
Cameron Davidson-Pilon's blog post on multi-armed bandits from a Bayesian perspective — draws on the same probabilistic programming intuition as his 'Bayesian Methods for Hackers' book. Frames bandits as the natural application of iterative belief updating.
Introducing R
Alyssa Frazee's introduction to R for people who don't yet know they need it — a gentle, motivated tour of why R is the right tool for statistical computing. Written by a biostatistician who uses it daily.
The Remarkable k-means++
Larry Wasserman's Normal Deviate blog post on k-means++ — the 2007 initialization trick from Arthur and Vassilvitskii that gives k-means an O(log k) approximation guarantee and better convergence in practice.
The Importance of Sequential Testing
Austin Rochford's introduction to sequential testing — the SPRT and Bayesian alternatives to fixed-horizon A/B tests that let you stop early when results are clear without inflating false positive rates.
Statistical Analysis Made Easy in Python
Randy Olson's tutorial on statistical analysis in Python using SciPy stats and pandas — t-tests, ANOVA, chi-squared, and more. A practical bridge from R's built-in stats to Python's ecosystem in 2012.
Drawing Inferences From Very Large Datasets
Econometrician Dave Giles on why large datasets make standard p-value thresholds useless — with N in the millions, almost any null hypothesis rejects, regardless of practical importance. A necessary corrective for data scientists drowning in statistical significance.
Deriving Formulas for Sample Size in A/B Tests
Mathematical derivation of the expected sample size needed in A/B tests using frequentist power analysis. Derives the N formula from effect size, significance level (α), and power (1-β) — useful for anyone designing experiments who wants to understand where 'you need at least X users' comes from.
The Mysterious Law That Governs the Size of Your City
io9 explainer on Zipf's law for city populations — the rank-size rule that holds across every country for a century: the largest city is roughly twice the next-largest, and so on. The pattern is empirically reliable but theoretically unexplained.
Bayesian Statistical Analysis with PyMC
PyTennessee 2013 presentation on Bayesian statistical analysis with PyMC — introducing probabilistic programming in Python as a practical alternative to frequentist methods. PyMC let practitioners write down generative models and get MCMC inference without implementing samplers from scratch.
An Introduction to Data Analysis — Statistics Done Wrong
Alex Reinhart's 'Statistics Done Wrong' introduction to data analysis — opens with the key insight that a p-value measures surprise, not correctness. A corrective for scientists trained in classical statistics who misinterpret their own results.
Everything Wrong With P-Values Under One Roof
A comprehensive critique of p-values and null hypothesis significance testing — cataloguing the ways researchers misinterpret and misuse them. Part of a growing 2013 literature on the replication crisis and statistical reform.
Nate Silver on Finding a Mentor, Teaching Yourself Statistics, and Not Settling
HBR interview with Nate Silver on finding mentors, self-teaching statistics, and not settling for work below your potential. Advice from the FiveThirtyEight founder at the peak of his post-2012-election fame.
Flipping a Coin: Bayesian Updating of Probability Distributions
A walkthrough of Bayesian probability updating using coin flipping — showing how a prior distribution over coin bias is updated with each flip observation. The cleanest possible introduction to Bayesian reasoning as a process.
Simpson's Paradox: Interactive Visualization
VUDLab's interactive visualization of Simpson's Paradox — showing how a trend that appears in every subgroup can reverse when the groups are combined. A crucial statistical phenomenon for anyone working with observational data.
Nate Silver Gets Real About Big Data
ReadWrite's coverage of Nate Silver pushing back on big data hype — arguing that more data doesn't automatically improve predictions, and that statistical rigor and good models matter more than raw volume. Silver had credibility from his 2012 election forecasting success.
How Data Changes Preconceptions About NFL Football
TechCrunch on how data analysis overturns conventional wisdom in NFL football — using statistical analysis to challenge received wisdom about weather, home field advantage, and other football beliefs. Part of the broader sports analytics wave that Moneyball had popularized.
Datashaping Analytics Book (ABbook5)
A self-published analytics/statistics PDF by Vincent Granville (datashaping.com) — one of his data science book resources available as a free download circa 2013. Granville was an early data science community builder who self-published extensively on applied analytics.
Bayesian Methods for Hackers
Cameron Davidson-Pilon's open-source book teaching Bayesian inference through computational examples in Python, using PyMC3 for probabilistic programming. The approach is computation-first rather than math-first — ideal for programmers who want to apply Bayesian reasoning without heavy statistics background.
The Central Limit Theorem — Visual Explanation
Victor Powell's interactive visualization of the Central Limit Theorem, showing how sample means converge to a normal distribution regardless of the underlying population distribution. A beautiful interactive demonstration that makes the theorem's implications visceral rather than abstract.
A Very Short History of Data Science
Gil Press's Forbes timeline tracing data science from John Tukey's 1962 'The Future of Data Analysis' through the 2000s emergence of the term. A useful historical grounding for understanding why 'data science' coalesced as a separate discipline rather than just being statistics.
Statistical Formulas for Programmers
Evan Miller's reference sheet of statistical formulas presented as code-friendly pseudocode rather than academic notation. A practical bridge between statistical theory and implementation, covering the formulas programmers actually need for A/B testing and product analytics.
Career Advice: How Do I Become a Data Scientist?
Quora's canonical 2013 answer on becoming a data scientist — one of the most-read career guides in the early data science field. A snapshot of what skills and background paths were considered credible entry points before formal data science degrees existed.
Bayes' Rule in Haskell, or Why Drug Tests Don't Work
Classic probabilistic reasoning example using drug tests to illustrate Bayes' rule: even a highly accurate test produces mostly false positives when the base rate of drug use is low. Implemented in Haskell to make conditional probability feel like simple if-statements.
Pundits: Stop Sounding Ignorant About Data
Andrew McAfee's HBR post calling out common misunderstandings in big data media coverage — conflating correlation with causation, treating anecdotes as data, and misusing statistical concepts. A 2013 data literacy argument aimed at commentators rather than practitioners.
The Dangers of Cargo Cult Data Science
Forbes piece on cargo cult data science — organizations adopting the trappings of data-driven decision-making (dashboards, models, data scientists) without the epistemological rigor that makes it actually work. A 2013 critique that remains current.
Don Turnbull's Data Science Book Recommendations
DataScholars post on Don Turnbull's data science book recommendations — a 2013 curated reading list for practitioners entering the field. A period artifact showing what an experienced data scientist thought was essential reading at the height of the big data hype cycle.
Data Analysis, Statistics, and Probability Overview
Annenberg Learner's Data Analysis, Statistics, and Probability course — a free online course covering statistical reasoning, data representation, and probability for educators and learners. A foundational resource for building statistical intuition before the MOOC era.
Introduction to Machine Learning — Alex Smola, CMU 2013
Alex Smola's Introduction to Machine Learning course at CMU (10-701, 2013) — a graduate-level survey of ML theory and methods from one of the field's top researchers. Course materials publicly available, covering optimization, probabilistic models, and learning theory.
Statistics for Genomics: Introduction to RNA-seq
A YouTube lecture series on statistical methods for RNA-seq analysis — covering the mathematical foundations behind differential expression analysis, normalization, and count modeling. A bioinformatics education resource from the early RNA-seq era.
Probability Theory — A Primer
Jeremy Kun's Math ∩ Programming blog post introducing probability theory from first principles — sample spaces, events, probability measures, conditional probability, and random variables. Part of his series making advanced mathematics accessible to programmers.
The Mathematical Hacker
Evan Miller's essay arguing that programmers who invest in mathematical fluency gain compounding advantages — because math enables them to evaluate methods rather than just apply them, and to work with uncertainty and probability naturally. The case for quantitative education in software.
High Dimensional Undirected Graphical Models
Larry Wasserman's 'Normal Deviate' blog post on high-dimensional undirected graphical models — a rigorous but accessible treatment of the statistical theory for learning sparse graphs from data when the number of variables exceeds the sample size. Core to modern genomics and causal inference.
Probability and Statistics Cookbook
Matthias Vallentin's probability and statistics cookbook — a dense reference PDF covering distributions, estimation, hypothesis testing, and Bayesian methods in concise formula sheets. The kind of reference you keep open in a second tab when doing statistical work.
So You Call Yourself a Data Scientist?
VentureBeat's 2012 examination of what 'data scientist' actually means — a job title proliferating faster than the field had consensus on its definition. Published at the height of the 'sexiest job of the 21st century' hype cycle.
Bayes' Theorem: Conditional Probabilities
A Vassarstats reference page on Bayes' Theorem and conditional probabilities. The theorem is the backbone of Bayesian reasoning: updating prior beliefs with new evidence to get a posterior probability.
The Miniature Earth: if Earth had 100 people
The Miniature Earth is a short video that reframes global statistics by imagining Earth as a village of 100 people. A classic early viral edu-video that makes global inequality concrete through proportional scale.