Bayes Dojo

Bayes Dojo helps you learn probability, statistics, and Bayesian inference by changing conditions and watching graphs respond. How often is an item actually defective after a positive inspection result? What changes when you collect more data? What can a sample tell you about a population? Explore a concrete example, change a condition, and read the explanation of what happened. Connect formulas with why a topic matters and when to use it. Start with one experiment • Begin with the recommended experiment on Home. • Use Experiment to change conditions, then Read to explore results, formulas, and assumptions. • Open the book icon for the purpose, method, and a concrete example. • Try a knowledge check, then continue to a related lesson. 11 Bayesian experiments • Interpret inspection results and base rates using natural frequencies. • Add evidence step by step and compare prior and posterior distributions. • Explore credible intervals, posterior probabilities, and predictions of future observations. • Try A/B decisions, expected loss, model checks, and expected information gain. • Continue to Bayesian regression, hierarchical models, and MCMC. 12 statistics experiments • Independence and mutually exclusive events, expectation and risk, density and area • Distribution approximations, sampling bias, and bootstrap resampling • Confidence intervals, statistical power, and multiple testing • Simpson's paradox, least-squares regression and residuals, and information coding Foundations that connect the ideas • Populations and samples, variance with divisors n and n−1, standard deviation and standard error • The law of large numbers and the central limit theorem • Likelihood, maximum likelihood estimation, Fisher information, and hypothesis testing • Self-information, entropy, mutual information, cross-entropy, and KL divergence • Ten probability distributions and how they relate Find the topic you need Choose a lesson, browse by purpose, or search the topic index. Search using either Japanese or English terms. Made for iPhone, iPad, and Mac Switch between Japanese and English in the app. Use portrait, landscape, and Split View on iPad. Layouts adapt to text size and available space. Lessons and calculations run on your device. No account or internet connection is needed for learning. The iPhone and iPad versions display banner ads. Ads, external references, and websites require a connection. The Mac version has no ads, and there are no in-app purchases. Bayes Dojo uses teaching examples and models with stated assumptions. Explore statistics for the first time or revisit the foundations behind your classes and research.