Understand the setting
See what the example is asking and what its terms mean. Start with the context behind a positive test or a defect rate.
Bayes Dojo
Learn from evidence, then predict and decide.
How do predictions and decisions change as evidence grows? Change a condition, watch the graph, then read the explanation. Connect Bayesian inference with the foundations of probability and statistics, one idea at a time.
Available on the App Store
How does evidence change your view?
A learning example: the probability that a coin lands heads.
Before observing dataAfter 7 heads and 3 tails
A Beta(1,1) prior becomes a Beta(8,4) posterior. The curves show density over p; the area under each is one.
Explore · Change · Understand
Start with one experiment.
Understand the example, change one condition, and connect what you see with why it happens.
Change one condition
Use a button or slider in Experiment. Find the part of the graph to watch, then compare what changes.
Read the reasoning
Use Read for results, formulas, and assumptions. The book icon explains why the topic matters and when to use it.
Curriculum
Bayes and statistics.
23 experiments, each with a question.
Eleven Bayesian experiments in three courses, plus twelve statistics experiments in three courses. Choose a question and revisit the foundations when you need them.
Bayes · Foundations · 4 experiments
Update your view with evidence
Why is a test’s detection rate different from the chance a positive item is defective?
Topics covered
- Test results and base rates
- Sequential updating
- Comparing priors
- Credible intervals and posterior probabilities
Bayes · Practice · 4 experiments
Predict, decide, and check
Predict future results, weigh the loss of a choice, and check whether a model fits.
Topics covered
- Posterior prediction
- A/B decisions and expected loss
- Model checks
- Expected information gain and experimental design
Bayes · Advanced · 3 experiments
Model uncertainty
Estimate a line, learn across groups, and approximate a posterior using samples.
Topics covered
- Bayesian regression
- Hierarchical models
- MCMC
Statistics · Probability · 4 experiments
Read randomness in a graph
Are mutually exclusive events independent? Is an average enough to choose?
Topics covered
- Independence and mutual exclusivity
- Expectation and risk
- Density and area
- Distribution approximations
Statistics · Inference · 5 experiments
What can a sample tell you?
Compare sampling bias, uncertainty in estimates, and the power to detect a difference.
Topics covered
- Sampling bias
- Bootstrap resampling
- Confidence intervals
- Statistical power
- Multiple testing
Statistics · Data & information · 3 experiments
Check your summaries
Can aggregation reverse a conclusion? What can a straight line explain?
Topics covered
- Simpson’s paradox
- Least-squares regression and residuals
- Information coding
Foundations
Connect the terms
to the foundations.
Use foundation lessons and the distribution reference to understand the ideas behind an experiment: its purpose, examples, and formulas.
Samples and estimation
Populations and samples, the law of large numbers, the central limit theorem, variance with divisors n and n−1, standard deviation, and standard error.
Likelihood and tests
Likelihood, maximum likelihood, Fisher information, and hypothesis testing. Understand what you estimate and what you compare.
Information
Self-information, entropy, mutual information, cross-entropy, and KL divergence.
Ten probability distributions
Bernoulli, binomial, normal, Poisson, exponential, gamma, chi-square, Student’s t, F, and beta distributions, and their relationships.
Find your next question
Find the idea you need.
Lesson catalogue
See each course, unit, and the topics it covers. Choose a lesson that matches your question.
Bilingual topic index
Search using Japanese or English terms and follow the links to related lessons.
Purpose behind each topic
Use the book icon for concrete examples of why a topic matters and when to use it.
Requirements & privacy
On iPhone, iPad, and Mac.
Requirements
Requires iOS / iPadOS 17 or later, or macOS 14 or later. Switch between Japanese and English in the app. Use portrait, landscape, and Split View on iPad.
Lessons and calculations run on your device. No account or internet connection is needed for learning. There are no in-app purchases.
Advertising and privacy
The iPhone and iPad versions show banner ads at the bottom of the screen. Lessons remain available when ads cannot be loaded. The Mac version has no ads.
Ads and external links require a connection. The privacy policy explains advertising SDK data handling and consent choices.
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