Explores the probability of extreme 'six sigma' events using the Student t distribution, showing it's not monotonic and depends heavily on degrees of freedom.
A statistical analysis of the classic board game Snakes & Ladders, modeling it as a Markov chain to calculate the expected game length.
Explores the mathematics of card shuffling, contrasting random 'rifle shuffles' with deterministic 'perfect shuffles' and their Python implementation.
A machine learning professor critiques the foundational concept of a 'data-generating distribution' and shares insights from teaching a truly distribution-free course.
A statistical reasoning test with three practical problems on sorting uncertain fractions, highlighting anomalies, and estimating population sizes.
Analyzing the probability of covering all birthdays in a group and the expected number of people needed, framed as the Coupon Collector's Problem.
Using R simulations to calculate birthday probabilities instead of complex probability math, with code examples.
An update on the polymath research project about non-transitive dice and its statistical implications for the Wilcoxon/Mann-Whitney test.
A detailed analysis of an optimal stopping problem involving drawing cards for reward, exploring mathematical strategies and first-principles reasoning.
Explains why pairwise independence of variables does not imply joint independence, using a chessboard as an intuitive counterexample.
Explores convolutions in probability theory, explaining how they combine distributions and compute sums of random variables.
A statistical analysis of estimating a normal distribution using binary (yes/no) predictions from multiple scientists, applied to a temperature forecasting problem.
A mathematical and computational exploration of the probability of a coin landing on its edge, inspired by Matt Parker's question about a 'three-sided coin'.
Explains how to apply Bayesian thinking and probability to critically analyze news articles and identify underlying biases.
Explores practical differences between Bayesian and Frequentist statistical methods using a sci-fi probability problem.
A tutorial on Probability and Statistics concepts, from basics to generalized linear models, presented at PyData NYC with Python examples.
Explains the mathematical derivation of logistic regression from Bayes' theorem, connecting fundamental statistics to machine learning.
A technical analysis verifying a statistical calculation from an XKCD comic, involving normal distribution probabilities and R code.
Explores the 'waiting time paradox' using probability, simulation, and real bus data to explain why average wait times often exceed the scheduled interval.
A technical article discussing debugging tricks for complex statistical models with symmetries, focusing on verification and small-sample testing.
