Bayesian Thinking for Analysts
Update beliefs with data using priors, likelihoods and posteriors you can explain
A taste of a lesson
A new page converted 7 of 20 visitors. With a uniform prior, what should I believe about its conversion rate?
Start with Beta(1, 1), the uniform prior. Add 7 successes to the first number and 13 failures to the second: the posterior is Beta(8, 14). Its mean is 8 divided by 22, about 0.36. With only 20 visitors the posterior is wide, roughly 0.18 to 0.57 for a 95 percent credible interval, so the rate is still very uncertain. Now try a sceptical prior, Beta(4, 36), which says 'around 10 percent'. What posterior mean do you get, and how different is it?
Written by the teacher as an example. In your lesson the tutor answers your own questions, and like any AI it can be wrong.
What you will be able to do
- Apply Bayes rule to update a belief with new evidence
- Update a beta prior for a rate by hand
- Build and interpret a credible interval
- Choose and stress test priors transparently
- Compare two variants with a posterior probability and expected difference
Lesson plan
- 1 Updating beliefs with counts Use Bayes rule on a simple example with natural frequencies. Start
- 2 Priors for a rate Represent beliefs about a rate with a beta distribution. Start
- 3 From prior to posterior Update a beta prior with observed successes and failures. Start
- 4 Credible intervals Summarise posterior uncertainty and phrase it correctly. Start
- 5 Choosing and testing priors Select priors defensibly and check how much they matter. Start
- 6 Comparing two variants Decide between options using posterior samples. Start
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About this tutor
An intermediate tutor for analysts who know basic statistics and want to reason the Bayesian way. You will start with Bayes rule on counts, then move to priors and posteriors for conversion rates using the beta binomial model, which you can update with a calculator. Lessons cover credible intervals, choosing and stress testing priors, comparing two variants by the probability one is better, and how Bayesian and frequentist answers differ in meaning. The tutor is neutral between schools of thought and shows where each is useful, including where Bayesian methods need heavier computation.
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About the teacher
Statistics in plain language, from averages to Bayesian reasoning
9 tutors 350 lessons taught Sample
I teach statistics to people who were put off by it the first time. My approach is to start from a question someone actually has, simulate or count our way to an answer, and only then name the formula. I have worked as an analyst on survey and health research projects, so I have a soft spot for messy samples,...
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