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1890 learning items

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Quiz

Philosophy: Frequentist vs. Bayesian Reasoning

Frequentist and Bayesian reasoning: distinguish repeated-sampling guarantees from probability distributions representing uncertainty about fixed unknown quantities. Compare confidence and credible statements, likelihood-based evidence, stopping rules, subjective information and the shared need for model criticism and calibration. Includes original single-select and multiselect scenarios, worked reasoning and explanations of each distractor. Prerequisites: Parts 01–23 or equivalent demonstrated outcomes. Authored from the saved Statistics & Probability syllabus; intended for progressive independent practice. Further reading: [Bayesian Data Analysis, 3rd edition](https://users.aalto.fi/~ave/BDA3.pdf).

statistics

Oct 26, 2026

20 questions

Quiz

Calibration, Predictive Uncertainty & Model Interpretation

Calibration, predictive uncertainty and model interpretation: evaluate probability forecasts using Brier score and log loss, diagnose reliability diagrams, choose cost-sensitive thresholds, interpret partial dependence cautiously and construct split conformal prediction intervals under exchangeability. Explore rare-class evaluation, data leakage and the limits of marginal coverage. Includes original single-select and multiselect scenarios, worked reasoning and explanations of each distractor. Prerequisites: classification, validation, conditional probability and neural-network generalization. Authored from the saved Statistics & Probability syllabus; intended for progressive independent practice. Further reading: [Probability calibration](https://scikit-learn.org/stable/modules/calibration.html), [Model evaluation](https://scikit-learn.org/stable/modules/model_evaluation.html), [Angelopoulos and Bates: Conformal prediction](https://arxiv.org/html/2107.07511v6), [Partial dependence and ICE](https://scikit-learn.org/stable/modules/partial_dependence.html).

statistics

Oct 26, 2026

20 questions

Quiz

Completeness, Ancillarity & UMVU Estimation

Study why complete sufficient statistics can identify unique unbiased estimators and establish independence from ancillary statistics. Original exercises combine factorial moments, completeness proofs, normal and scale-family examples, and the scope of UMVU claims. Prerequisites: sufficiency, conditional expectation, Rao–Blackwellization and basic integration. 20 original single-select and multiselect questions progress from understanding through worked applications to assumption checks and advanced challenges. Detailed explanations address each alternative. Study the prerequisites before attempting the final challenges.

statistics

Oct 26, 2026

20 questions

Quiz

Rao-Blackwell Theorem, MVUE & Cramér-Rao Lower Bound

Connect conditional expectation, information and the limits of unbiased estimation. Compute Rao–Blackwell improvements and information bounds, then investigate equality, nuisance parameters and moving-support exceptions. Prerequisites: sufficiency, likelihood derivatives, covariance and matrix inversion. 25 original single-select and multiselect questions progress from understanding through worked applications to assumption checks and advanced challenges. Detailed explanations address each alternative. Study the prerequisites before attempting the final challenges.

statistics

Oct 26, 2026

25 questions

Quiz

Sufficiency & The Factorization Criterion

Learn to reduce data without losing parameter information inside a specified model. Factor likelihoods for discrete, lifetime, normal and bounded-support samples, then examine minimality, recoverable transformations and lossy storage. Prerequisites: joint densities, conditional distributions and likelihood algebra. 25 original single-select and multiselect questions progress from understanding through worked applications to assumption checks and advanced challenges. Detailed explanations address each alternative. Study the prerequisites before attempting the final challenges.

statistics

Oct 26, 2026

25 questions

Quiz

Consistency & Relative Efficiency

Analyze when estimators concentrate around a fixed target and when that claim is weaker than moment convergence. Work through probability bounds, variance-ratio conventions, optimal combinations, differing rates and equal-cost comparisons. Prerequisites: expectation, variance, probability convergence, basic asymptotic distributions and squared-error risk. 25 original single-select and multiselect questions progress from understanding through worked applications to assumption checks and advanced challenges. Detailed explanations address each alternative. Study the prerequisites before attempting the final challenges.

statistics

Oct 26, 2026

25 questions

Quiz

Stochastic Processes & Measure-Theoretic Orientation

Build an orientation to stochastic processes and measure-based probability using Poisson arrivals, independent thinning, random walks and martingale examples. Practice sigma-algebra closure, probability measures and almost-sure reasoning; this survey does not replace a graduate probability sequence. Prerequisites: probability, statistical inference and the preceding core curriculum. Original single-select and multiselect scenarios progress from interpretation to worked applications and assumption-sensitive challenges. Detailed solutions explain the alternatives; this is educational statistical practice.

statistics

Oct 26, 2026

20 questions

Quiz

Statistical Process Control & Reliability

Monitor stable processes using Shewhart, EWMA and CUSUM ideas, distinguish specification limits from control limits, and calculate process capability under stated assumptions. Connect operational monitoring to reliability and failure-time models. Prerequisites: probability, statistical inference and the preceding core curriculum. Original single-select and multiselect scenarios progress from interpretation to worked applications and assumption-sensitive challenges. Detailed solutions explain the alternatives; this is educational statistical practice.

statistics

Oct 26, 2026

20 questions

Quiz

Multinomial & Ordinal Logistic Regression

Extend logistic regression to nominal and ordered outcomes. Practice baseline-category logits, probability normalization, cumulative logit predictions and proportional-odds interpretations with explicit conventions. Prerequisites: binary logistic regression, likelihood and categorical coding. Advanced problems examine reference changes, valid cumulative probabilities, parameter restrictions and evidence against parallel slopes. Further reading: [ORDINAL reference](https://stats.oarc.ucla.edu/stata/dae/ordered-logistic-regression/), [Nominal-response reference](https://stats.oarc.ucla.edu/mplus/dae/multinomiallogistic-regression/).

statistics

Oct 26, 2026

20 questions

Quiz

Model Discrimination & Classification Performance

Evaluate binary classifiers using confusion matrices, sensitivity, specificity, precision, F1, ROC curves and AUC. Original operational scenarios connect thresholds to error costs and class imbalance. Prerequisites: binary prediction, conditional probability and basic proportions. Includes numerical exercises and challenges on ranking, calibration, prevalence shift and validation leakage. Further reading: [METRICS reference](https://scikit-learn.org/stable/modules/model_evaluation.html).

statistics

Oct 26, 2026

30 questions

Quiz

Estimation & Statistical Inference in Logistic Regression

Fit and assess logistic regression through likelihood, numerical optimization and statistical inference. Work through Bernoulli contributions, scores, IRLS, Wald calculations, likelihood-ratio comparisons, deviance, separation and sparse-data diagnostics. Prerequisites: logistic formulation, likelihood, matrix regression and asymptotic testing. Challenges emphasize regularity conditions, convergence evidence and defensible remedies. Further reading: [GLM reference](https://ucla-biostat-200c-2020spring.github.io/slides/09-glm/glm.html).

statistics

Oct 26, 2026

30 questions

Quiz

Logistic Regression Formulation & The Logit Link

Develop logistic regression from odds and log-odds to adjusted probability predictions. Practice continuous and categorical contrasts, predictor transformations, interactions, and careful distinctions among odds ratios, risk ratios and probability changes. Prerequisites: probability, algebra, regression and the linear probability model. Includes single-select and multiselect problems, worked calculations, and assumption-based challenges. Further reading: [ISL reference](https://www.statlearning.com/s/ISLRSeventhPrinting.pdf).

statistics

Oct 26, 2026

30 questions