Statistics Quest

Advanced Foundations

Bayesian inference, multivariate methods and causal thinking.

Bayesian updating with conjugate priors, credible intervals and Bayesian A/B analysis; principal component analysis; classification evaluation; and an introduction to causal inference and the limits of statistical models.

Lessons

  1. 1Bayesian thinking: prior, likelihood, posteriorCombine a prior distribution with the likelihood of observed data to obtain a posterior distribution, and explain how the prior and the data share the influence.35 minFree
  2. 2Beta–binomial updatingUpdate a Beta prior for a proportion with binomial data, interpret the posterior, check its sensitivity to the prior, and predict future outcomes with the posterior predictive distribution.40 minMembers
  3. 3Credible intervalsCompute equal-tailed and highest-posterior-density credible intervals and posterior tail probabilities, and interpret them correctly — including how they differ from confidence intervals.35 minMembers
  4. 4Bayesian A/B testingAnalyse an A/B test with Beta posteriors — P(B > A), the posterior of the difference and expected loss — and make a decision while respecting the method's assumptions and limits.40 minMembers
  5. 5Principal component analysisRun and interpret a principal component analysis: decide whether to standardise, read variance explained and a scree plot, interpret loadings (allowing for arbitrary signs) and scores, and state what PCA cannot do.40 minMembers
  6. 6Evaluating classifiersEvaluate a binary classifier with a confusion matrix and the right metrics, explain why accuracy misleads under class imbalance, read ROC curves and AUC, choose a threshold from the costs of errors, and avoid leakage.45 minMembers
  7. 7Causal inference: potential outcomes and causal diagramsDefine causal effects with potential outcomes, use simple causal diagrams to decide what to adjust for, and explain what randomisation and regression adjustment can and cannot achieve.45 minMembers
  8. 8Model limitations and honest reportingIdentify the limitations of a statistical model — extrapolation, overfitting, violated assumptions, data drift and confounding — and report results with honest uncertainty and scope.35 minMembers