stat wiki

A study wiki for data analysis, probability, stochastic processes, statistical learning, statistical inference, and STAT3500/7500: 77 chapters and 526 questions, 479 of them with worked answers. Every chapter lists the questions on its topic, and every question links back to its chapter. Use the search box at the top to find any term, or open a random question to test yourself.

Probability

• Random experiments and probability
• Random variables and distributions
• Simulation
• Joint distributions
• Functions of random variables and limit theorems
• Markov chains
• Reliability

90 questions →

Stochastic processes

• Stochastic processes
• Galton–Watson branching
• Random walks and first passage
• Discrete-time Markov chains
• Classes, recurrence, and reversibility
• Poisson processes
• Continuous-time Markov chains
• Birth–death chains and queues
• Probability spaces and events
• Random variables and laws
• Expectation and convergence
• A first look at extremes

35 questions →

Statistical inference

• Statistical inference
• Estimation
• Confidence intervals
• Hypothesis tests
• Chi-squared tests
• Linear regression
• Analysis of variance

36 questions →

Data analysis

• Studies, data, and evidence
• Descriptive statistics
• Using R
• Estimation examples
• Testing examples
• Analysis of variance examples
• Regression examples
• Linear model examples
• Chi-squared examples

30 questions →

Bayesian statistics

• Bayesian foundations
• The Beta–Binomial model
• Conjugate analysis for normal models
• Markov chains, Gibbs sampling, and Metropolis–Hastings
• Categorical data and the Dirichlet distribution
• Bayesian hypotheses and model comparison
• Exponential families and conjugacy
• Hierarchical Bayes
• Bayesian linear regression

133 questions →

Generalised linear models

• Introduction to generalised linear models
• Standard errors, and models for counts
• Underdispersion, positive responses, and quasi-likelihood
• Categorical responses
• Paired comparisons, and how far a fit is from the data
• Probability-integral residuals

29 questions →

Smoothing

• Smooth means
• Additive smooths

7 questions →

Statistical learning

• Covariance and the multivariate normal
• Estimation and inference for the multivariate normal
• Principal component analysis
• K-means clustering
• Mixtures and the EM algorithm
• Model selection for stochastic models
• Hierarchical clustering and kernel density estimation
• Statistical classifiers and discriminant analysis
• Estimating error rates
• Logistic regression
• Nearest neighbours
• Classification trees
• Ensembles, random forests, and boosting
• Neural units
• Backpropagation
• Networks in practice
• Support vector machines
• High-dimensional analysis
• Graphical models

144 questions →

Correlated data

• Random intercepts
• Random slopes, and a binary mixed model
• Marginal models, and two responses at once
• Three species on one hillside

13 questions →

Time series

• Dependence along a series
• Forecasting

9 questions →

Final preparation

• How to use the final preparation
• Bayesian final questions
• Applied final questions

22 questions →

Question bank

• By topic
• Random question

Reference

• Common distributions
• Formula lookup

How to study with it

1. Read a chapter. The contents on the right jump between its sections.
2. Scroll to Questions on this topic at the end and open one.
3. Attempt it, then open Worked answer at the bottom of the question page.
4. Use ‹ previous and next › at the top of a question to move through the questions on the same topic.

The source is on GitHub. Every change pushed there rebuilds this site.