Subject
30 entries
Probability
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.
Probabilistic Machine Learning (Kevin Murphy)
Kevin Murphy's Probabilistic Machine Learning book series — a comprehensive treatment of ML through a probabilistic/Bayesian lens, freely available online. The 2012 original (MLPP) and its 2022 follow-ups are standard graduate-level references.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
What Bayesianism Taught Me
A LessWrong post on what Bayesian reasoning changed about the author's thinking — not the mechanics of Bayes' theorem but the epistemic habits it instills. Treating beliefs as probability distributions rather than binary true/false is the core insight.
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.
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.
How Airbnb Used Conditional Probability Models to Improve Search
How Airbnb used conditional probability models and data visualization to improve search ranking — an early public example of a major consumer company describing ML-driven search personalization. Significant for its transparency about the modeling approach.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.