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Browse all available quizzes, quizbooks, articles, textbooks, SynLearn templates, and SynPrep practice tracks.

1890 learning items

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Quiz

Computational Bayesian Statistics: Markov Chain Monte Carlo (MCMC)

Learn how posterior computation works and how to judge the reliability of its output. Calculate Metropolis-Hastings acceptance probabilities, compare Gibbs and Hamiltonian methods, and interpret chain agreement, bulk and tail ESS, Monte Carlo error, divergences and energy diagnostics. Prerequisites: conditional distributions, posterior densities, gradients and basic Markov-chain ideas. Includes diagnostic tradeoffs and counterexamples to simplistic convergence claims. Single-select and multiselect practice includes worked explanations and distractor rationales. Study sources: Stan: Posterior Analysis; Stan: MCMC Sampling. Photo by ThisIsEngineering on Pexels.

statistics

Oct 26, 2026

25 questions

Quiz

Posterior Summaries & Credible Intervals

Build a careful vocabulary for Bayesian posterior summaries and credible intervals. Practice exact calculations, simulation quantiles, equal-tailed and highest-density regions, transformed parameters, skewness and multimodality. Prerequisites: probability distributions, Bayes updating, quantiles and basic integration. Worked explanations distinguish inferential uncertainty from Monte Carlo precision and extend to joint coverage and disconnected support. Single-select and multiselect practice includes worked explanations and distractor rationales. Study sources: Bayesian Data Analysis, Sections 2.3 and 3.1. Photo by RDNE Stock project on Pexels.

statistics

Oct 26, 2026

25 questions

Quiz

statistics

Neural Networks & Statistical Generalization

Explore Neural Networks & Statistical Generalization through 20 original single-select and multiselect questions, from core understanding to worked applications, assumption checks and advanced diagnostic challenges. Prerequisites: the preceding Statistics curriculum, including probability, conditional distributions, regression, model validation and regularization. Practice goals: Explain units, activations and output choices; Calculate forward passes, parameter counts and gradients; Assess regularization, gradient flow and validation; Analyze symmetries and interpolation beyond training data; Distinguish derivative computation from optimization guarantees; Evaluate data requirements and unit-of-deployment sampling. Explanations work through the reasoning and address the alternatives. Further reading: [neural_networks_supervised](https://scikit-learn.org/stable/modules/neural_networks_supervised.html).

statistics

Oct 26, 2026

20 questions

Quiz

statistics

Boosting & Support Vector Machines

Explore Boosting & Support Vector Machines through 20 original single-select and multiselect questions, from core understanding to worked applications, assumption checks and advanced diagnostic challenges. Prerequisites: the preceding Statistics curriculum, including probability, conditional distributions, regression, model validation and regularization. Practice goals: Explain boosting stages and margin classifiers; Calculate loss gradients, hinge losses and margin widths; Assess kernels, tuning and ensemble structure; Analyze general-loss boosting and evaluation risks; Understand support-vector representations; Interpret soft-margin robustness and data provenance. Explanations work through the reasoning and address the alternatives. Further reading: [ensemble](https://scikit-learn.org/stable/modules/ensemble.html); [svm](https://scikit-learn.org/stable/modules/svm.html).

statistics

Oct 26, 2026

20 questions

Quiz

statistics

Trees, Bagging & Random Forests

Explore Trees, Bagging & Random Forests through 20 original single-select and multiselect questions, from core understanding to worked applications, assumption checks and advanced diagnostic challenges. Prerequisites: the preceding Statistics curriculum, including probability, conditional distributions, regression, model validation and regularization. Practice goals: Explain tree predictions and bootstrap aggregation; Compute impurity gains, residual reductions and OOB probabilities; Assess pruning, ensemble variance and feature importance; Diagnose interactions, OOB selection and deployment leakage; Analyze tree invariances and extrapolation; Distinguish forest diversity from additional Monte Carlo averaging. Explanations work through the reasoning and address the alternatives. Further reading: [tree](https://scikit-learn.org/stable/modules/tree.html); [ensemble](https://scikit-learn.org/stable/modules/ensemble.html).

statistics

Oct 26, 2026

20 questions

Quiz

Markov Chains & Simulation Foundations

Finite Markov chains and simulation foundations: interpret transition matrices, calculate multi-step probabilities and stationary distributions, and check irreducibility, aperiodicity and detailed balance. Distinguish stationarity from convergence and independent sampling, simulate transitions with uniform random numbers and analyze counterexamples to common long-run claims. Includes original single-select and multiselect scenarios, worked reasoning and explanations of each distractor. Prerequisites: conjugate models, probability vectors and basic matrix multiplication. Authored from the saved Statistics & Probability syllabus; intended for progressive independent practice. Further reading: [Harvard Stat 110: Markov chains](https://stat110.hsites.harvard.edu/resource/markov-chains).

statistics

Oct 26, 2026

20 questions

Quiz

The Bias-Variance Tradeoff in High Dimensions

Understand why flexible regression can become unstable as predictor dimension approaches sample size. Work with rank, interpolation, bias-variance decomposition, shrinkage and sparse high-dimensional neighborhoods. Prerequisites: linear regression, matrices, expectation and variance. Problems emphasize precise conditions for nonuniqueness, prediction uncertainty, validation and the limits of training fit. Detailed ridge and lasso mechanics are reserved for their later questionsets. Further reading: [ISL reference](https://www.statlearning.com/s/ISLRSeventhPrinting.pdf).

statistics

Oct 26, 2026

20 questions

Quiz

Overdispersion & Negative Binomial Regression

Investigate count variation beyond a Poisson model. Work through Pearson dispersion, hidden rate heterogeneity, Gamma-Poisson mixtures, negative-binomial variance and zero-inflated models. Prerequisites: Poisson regression, conditional expectation and variance, likelihood and GLMs. Challenges distinguish modeling mean structure, dispersion, dependence and structural zeros rather than choosing models from one pooled statistic. Further reading: [NB reference](https://www.statsmodels.org/stable/generated/statsmodels.genmod.families.family.NegativeBinomial.html), [GLM family reference](https://stat.ethz.ch/R-manual/R-devel/library/stats/html/family.html), [ZIP reference](https://www.statsmodels.org/stable/generated/statsmodels.discrete.count_model.ZeroInflatedPoisson.html).

statistics

Oct 26, 2026

20 questions

Quiz

statistics

Nearest Neighbours & Generative Classification

Explore Nearest Neighbours & Generative Classification through 20 original single-select and multiselect questions, from core understanding to worked applications, assumption checks and advanced diagnostic challenges. Prerequisites: the preceding Statistics curriculum, including probability, conditional distributions, regression, model validation and regularization. Practice goals: Interpret KNN rules and class-conditional Gaussian parameters; Calculate posterior decisions and compare classifier assumptions; Diagnose imbalance, covariance estimation and dependent features; Evaluate transfer and asymptotic neighborhood choices; Analyze cost-sensitive decisions; Assess the limitations of sparse class-conditional samples. Explanations work through the reasoning and address the alternatives. Further reading: [neighbors](https://scikit-learn.org/stable/modules/neighbors.html); [lda_qda](https://scikit-learn.org/stable/modules/lda_qda.html); [naive_bayes](https://scikit-learn.org/stable/modules/naive_bayes.html).

statistics

Oct 26, 2026

20 questions

Quiz

statistics

Density Estimation, Local Regression & Splines

Explore Density Estimation, Local Regression & Splines through 20 original single-select and multiselect questions, from core understanding to worked applications, assumption checks and advanced diagnostic challenges. Prerequisites: the preceding Statistics curriculum, including probability, conditional distributions, regression, model validation and regularization. Practice goals: Interpret density plots and local smoothing; Calculate normalized densities and local means; Explain spline continuity, curvature penalties and natural boundaries; Diagnose additivity, boundary effects and high-dimensional smoothing; Analyze linear reproduction and smooth-term identification; Tune smoothing strength and distinguish basis capacity from effective flexibility. Explanations work through the reasoning and address the alternatives. Further reading: [density](https://scikit-learn.org/stable/modules/density.html); [smooth.spline](https://stat.ethz.ch/R-manual/R-devel/library/stats/html/smooth.spline.html); [loess](https://stat.ethz.ch/R-manual/R-devel/library/stats/html/loess.html); [gam](https://stat.ethz.ch/R-manual/R-devel/library/mgcv/html/gam.html).

statistics

Oct 26, 2026

20 questions

Quiz

statistics

Information Criteria: AIC, BIC & Mallows' Cp

Explore Information Criteria: AIC, BIC & Mallows' Cp through 20 original single-select and multiselect questions, from core understanding to worked applications, assumption checks and advanced diagnostic challenges. Prerequisites: linear regression, matrix algebra, calculus, bias-variance reasoning and the preceding Part 22 material. Practice goals: Define comparable AIC and BIC scores and parameter counts; Assess likelihood comparability and noise estimation; Compute criteria, differences and relative weights; Diagnose search, transformation and interpretation failures; Evaluate asymptotic claims and selection-aware assessment; Interpret Cp and its sampling behavior. Explanations work through the reasoning and address the alternatives. Further reading: [linear_model](https://scikit-learn.org/stable/modules/linear_model.html).

statistics

Oct 26, 2026

20 questions

Quiz

statistics

Lasso Regression (L1 Regularization) & Elastic Net

Explore Lasso Regression (L1 Regularization) & Elastic Net through 25 original single-select and multiselect questions, from core understanding to worked applications, assumption checks and advanced diagnostic challenges. Prerequisites: linear regression, matrix algebra, calculus, bias-variance reasoning and the preceding Part 22 material. Practice goals: Interpret L1 geometry, sparsity and penalty magnitudes; Explain elastic-net stabilization and grouping; Scale predictors and validate selection procedures; Derive soft-threshold and coordinate updates; Apply optimality conditions and assess selection instability; Analyze nonuniqueness, rotation dependence and support recovery. Explanations work through the reasoning and address the alternatives. Further reading: [linear_model](https://scikit-learn.org/stable/modules/linear_model.html).

statistics

Oct 26, 2026

25 questions