Questions by topic

The same 557 questions as the question bank, grouped under the chapter each one belongs to. 510 have a worked answer.

A chapter is beginner when it uses only events, variables, samples, and tables. It is intermediate when it adds one method, such as estimation, regression, a prior, or a standard classifier. It is advanced when that method is already assumed. A question has the level of its chapter.

Probability

90 questions in this part.

Random experiments and probability

17 questions.

Question	Level	Answer
Three coin tosses	Beginner	✓
Weights on the two coin spaces	Beginner	✓
Drawing from 365 balls	Beginner	✓
A lower bound on an intersection	Beginner	✓
Fifty-four distinct birthdays	Beginner	✓
Matching faces	Beginner	✓
Three cards in order	Beginner	✓
A point drawn from the unit interval	Beginner	✓
Three people, one birthday	Beginner	✓
One of each court card	Beginner	✓
Three brothers in a random split	Beginner	✓
Binary vectors with five ones	Beginner	✓
Five balls out of twenty	Beginner	✓
A one received on a noisy channel	Beginner	✓
A zero received	Beginner	✓
Information about one die	Beginner	✓
A channel with unequal inputs	Beginner	✓

Random variables and distributions

27 questions.

Question	Level	Answer
The smaller face	Beginner	✓
Ten voters	Beginner	✓
The larger coordinate	Beginner	✓
A cubic distribution function	Beginner	✓
Twenty fair tosses	Beginner	✓
Waiting for double six	Beginner	✓
Ten balls in three boxes	Beginner	✓
The sum of two dice	Beginner	✓
The waiting time itself	Beginner	✓
Distance to the centre	Beginner	✓
Five draws with replacement	Beginner	✓
Five draws without replacement	Beginner	✓
Particles in an hour	Beginner	✓
Five years of an exponential lifetime	Beginner	✓
Three-point expectation	Beginner	✓
Recovering the second moment	Beginner	✓
Expected number of red balls	Beginner	✓
Variance on the unit interval	Beginner	✓
An affine image of a uniform variable	Beginner	✓
Expected wait for double six	Beginner	✓
Groups of three	Beginner	✓
A memoryless component	Beginner	✓
Why a normal variance is \sigma^2	Beginner	✓
Exponential moments from the transform	Beginner	✓
A game on the sum of two dice	Beginner	✓
Two components with the same mean life	Beginner	✓
A game on the smaller face	Beginner	✓

Simulation

4 questions.

Question	Level	Answer
Draws from an exponential law	Beginner	✓
Draws from a uniform interval	Beginner	✓
Rescaling a standard normal draw	Beginner	✓
A shifted exponential density	Beginner	✓

Joint distributions

8 questions.

Question	Level	Answer
Minimum and average of uniform draws	Intermediate	✓
A joint table	Intermediate	✓
A probability as an integral	Intermediate	✓
Distribution function of a maximum	Intermediate	✓
One weight, or six weights	Intermediate	✓
A product density	Intermediate	✓
A point in a triangle	Intermediate	✓
Signs and their sum	Intermediate	✓

Functions of random variables and limit theorems

21 questions.

Question	Level	Answer
The square of a binomial count	Intermediate	✓
The square of a uniform variable	Intermediate	✓
An affine image of a standard normal	Intermediate	✓
Two standard normal probabilities	Intermediate	✓
Probabilities for a shifted normal	Intermediate	✓
An affine image of an exponential density	Intermediate	✓
A normal approximation on an interval	Intermediate	✓
Sum and proportion of two exponentials	Intermediate	✓
The mean of repeated voltage readings	Intermediate	✓
A normal approximation in the tail	Intermediate	✓
A quadratic function of a uniform variable	Intermediate	✓
An affine image of a uniform variable	Intermediate	✓
A normal law with mean 2	Intermediate	✓
State the probability functions	Intermediate	✓
Partial sums of standard normals	Intermediate	✓
A lift and a weight limit	Intermediate	✓
Thickness of a circuit board	Intermediate	✓
The sum of uniform draws	Intermediate	✓
Paying the square of the number of heads	Intermediate	✓
A sieve for blueberries	Intermediate	✓
Ten successive exponential components	Intermediate	✓

Markov chains

6 questions.

Question	Level	Answer
Two steps of a three-state chain	Intermediate	✓
The limit of the three-state chain	Intermediate	✓
Any two-state chain	Intermediate	✓
A chain that never settles	Intermediate	✓
A walk with a floor	Intermediate	✓
Where a random walk can be	Intermediate	✓

Reliability

7 questions.

Question	Level	Answer
Three components, one of them essential	Intermediate	✓
Structure of a k-out-of-n system	Intermediate	✓
Pivoting the bridge	Intermediate	✓
Paths and cuts of the bridge	Intermediate	✓
A string of twenty bulbs	Intermediate	✓
Mean life as an integral of survival	Intermediate	✓
Survival from the hazard	Intermediate	✓

Stochastic processes

35 questions in this part.

Stochastic processes

2 questions.

Question	Level	Answer
Same marginals, different joints	Advanced	✓
Stationary increments are not a fixed level	Advanced	✓

Galton–Watson branching

3 questions.

Question	Level	Answer
A critical offspring law	Advanced	✓
Several ancestors	Advanced	✓
The variance recurrence	Advanced	✓

Random walks and first passage

3 questions.

Question	Level	Answer
A fair walk between 0 and 8	Advanced	✓
A biased walk on four steps	Advanced	✓
Checking the duration formula	Advanced	✓

Discrete-time Markov chains

3 questions.

Question	Level	Answer
Two steps and the stationary law	Advanced	✓
A deterministic three-cycle	Advanced	✓
A doubly stochastic matrix	Advanced	✓

Classes, recurrence, and reversibility

3 questions.

Question	Level	Answer
One closed class	Advanced	✓
A walk on a path of four vertices	Advanced	✓
Birth–death balance on three states	Advanced	✓

Poisson processes

3 questions.

Question	Level	Answer
Counts and a first wait	Advanced	✓
Three events in two hours	Advanced	✓
Distance to the nearest point	Advanced	✓

Continuous-time Markov chains

3 questions.

Question	Level	Answer
A two-state chain in continuous time	Advanced	✓
Generator and jump chain	Advanced	✓
Why a generator row sums to zero	Advanced	✓

Birth–death chains and queues

3 questions.

Question	Level	Answer
An M/M/1 queue	Advanced	✓
An M/M/∞ system	Advanced	✓
Two machines, equal rates	Advanced	✓

Probability spaces and events

3 questions.

Question	Level	Answer
The algebra generated by two sets	Advanced	✓
Two series of events	Advanced	✓
Continuity from above	Advanced	✓

Random variables and laws

3 questions.

Question	Level	Answer
Positive and negative parts	Advanced	✓
Same margins, two joints	Advanced	✓
A function that is not a distribution function	Advanced	✓

Expectation and convergence

3 questions.

Question	Level	Answer
L2 convergence and probability	Advanced	✓
A spike that keeps its mean	Advanced	✓
A bound for a sample proportion	Advanced	✓

A first look at extremes

3 questions.

Question	Level	Answer
The expected maximum of n uniforms	Advanced	✓
Scaling an exponential maximum	Advanced	✓
A heavier sample and its maximum	Advanced	✓

Statistical inference

55 questions in this part.

Statistical inference

4 questions.

Question	Level	Answer
Summaries of ten cartons	Intermediate	✓
Which of these are statistics?	Intermediate	✓
The expectation of the sample variance	Intermediate	✓
A squared t variable	Intermediate	✓

Estimation

6 questions.

Question	Level	Answer
Normal maximum likelihood estimates	Intermediate	✓
Bias of the two variance estimators	Intermediate	✓
An exponential rate	Intermediate	✓
A Poisson mean	Intermediate	✓
A shrunken sample mean	Intermediate	✓
No uniform winner	Intermediate	✓

Information and bounds

2 questions.

Question	Level	Answer
Information for a Poisson mean	Advanced	✓
Where the bound does not apply	Advanced	✓

Rao–Blackwell and UMVU

2 questions.

Question	Level	Answer
An unbiased Poisson probability	Advanced	✓
Why the conditional expectation is better	Advanced	✓

Large-sample estimation

2 questions.

Question	Level	Answer
How many more observations the median needs	Advanced	✓
A probability from a Poisson mean	Advanced	✓

Confidence intervals

6 questions.

Question	Level	Answer
A proportion in a poll	Intermediate	✓
The interval for a normal mean	Intermediate	✓
Two standard errors	Intermediate	✓
Lost hours after a safety programme	Intermediate	✓
Checking equal variances	Intermediate	✓
Sizing a poll	Intermediate	✓

Hypothesis tests

6 questions.

Question	Level	Answer
A critical region for a known variance	Intermediate	✓
Power of a serve test	Intermediate	✓
How small a variance?	Intermediate	✓
Paired or two-sample?	Intermediate	✓
Tyre wear on five cars	Intermediate	✓
A one-sided sign test	Intermediate	✓

Most powerful tests

2 questions.

Question	Level	Answer
A critical value from the lemma	Advanced	✓
Why the two-sided test is not UMP	Advanced	✓

Generalised likelihood-ratio tests

2 questions.

Question	Level	Answer
The ratio depends only on the between sum of squares	Advanced	✓
One term of the expansion	Advanced	✓

Chi-squared tests

4 questions.

Question	Level	Answer
A 1:2:1 phenotype ratio	Intermediate	✓
Is the die fair?	Intermediate	✓
A two-by-two table is a two-proportion test	Intermediate	✓
Counting degrees of freedom	Intermediate	✓

Exact tests for tables

2 questions.

Question	Level	Answer
A smaller table by hand	Advanced	✓
Which hypothesis is it?	Advanced	✓

Linear regression

5 questions.

Question	Level	Answer
Normal equations for a straight line	Intermediate	✓
A line through the origin	Intermediate	✓
How much do the ads explain?	Intermediate	✓
Where is the prediction interval narrowest?	Intermediate	✓
The correlation test is the slope test	Intermediate	✓

Analysis of variance

6 questions.

Question	Level	Answer
Heart rates in four age groups	Intermediate	✓
A Tukey interval for two varieties	Intermediate	✓
Tips and coupons	Intermediate	✓
Two treatments in blocks	Intermediate	✓
A contrast among the corn varieties	Intermediate	✓
Two groups	Intermediate	✓

Linear hypotheses

2 questions.

Question	Level	Answer
Dropping a slope	Advanced	✓
How many restrictions?	Advanced	✓

Two-factor analysis of variance

2 questions.

Question	Level	Answer
Read the reference cell	Intermediate	✓
An interaction sum of squares	Intermediate	✓

Predictive values of a test

2 questions.

Question	Level	Answer
A rare condition	Intermediate	✓
The matching negative predictive value	Intermediate	✓

Data analysis

30 questions in this part.

Studies, data, and evidence

6 questions.

Question	Level	Answer
Alice’s heart-rate changes	Beginner	✓
Randomising twenty people	Beginner	✓
What a randomised trial does not need to record	Beginner	✓
Facial tumours in Tasmanian devils	Beginner	✓
A dose comparison for middle-of-the-night insomnia	Beginner	✓
Alcohol and school attendance	Beginner	✓

Descriptive statistics

2 questions.

Question	Level	Answer
Classifying variables in a nutrition survey	Beginner	✓
Reading a correlation	Beginner	✓

Estimation examples

7 questions.

Question	Level	Answer
Ten normal observations	Intermediate	✓
Household spending on fuel	Intermediate	✓
Narrowing a pilot interval	Intermediate	✓
Printer paper	Intermediate	✓
Hours of sleep	Intermediate	✓
A difference of proportions	Intermediate	✓
Variance of a fill volume	Intermediate	✓

Testing examples

6 questions.

Question	Level	Answer
Caffeine in a cola	Intermediate	✓
A later poll on leaving	Intermediate	✓
Steel rod diameters	Intermediate	✓
A shuffling machine	Intermediate	✓
Two proportions	Intermediate	✓
Home-ground wins	Intermediate	✓

Analysis of variance examples

2 questions.

Question	Level	Answer
Haemoglobin and sickle-cell type	Intermediate	✓
Five treatments, ten pairs	Intermediate	✓

Regression examples

3 questions.

Question	Level	Answer
Height and age of pine trees	Intermediate	✓
Birth weight and mother’s age	Intermediate	✓
Rain, food, and orange yield	Intermediate	✓

Linear model examples

2 questions.

Question	Level	Answer
How far sharks swim	Intermediate	✓
Wages, class, and gender	Intermediate	✓

Chi-squared examples

2 questions.

Question	Level	Answer
Possums in five areas	Intermediate	✓
Genotype and mating success	Intermediate	✓

Using R

12 questions in this part.

Using R

1 question.

Question	Level	Answer
Two fits on different rows	Beginner	✓

Exploratory data analysis in R

1 question.

Question	Level	Answer
What one row of the air-quality table is	Beginner	✓

Probability and simulation in R

1 question.

Question	Level	Answer
A point mass is not an interval probability	Beginner	✓

Bootstrap and numerical methods in R

1 question.

Question	Level	Answer
Which unit the bootstrap draws	Intermediate	✓

Mixtures and clustering in R

1 question.

Question	Level	Answer
A label that was not in the fit	Intermediate	✓

Bayesian computation in R

1 question.

Question	Level	Answer
The posterior mean is not the observed rate	Advanced	✓

Fitted models as objects

1 question.

Question	Level	Answer
An interval for the mean and an interval for a new day	Intermediate	✓

Generalised linear models in R

1 question.

Question	Level	Answer
What a log-link coefficient multiplies	Intermediate	✓

Generalised additive models in R

1 question.

Question	Level	Answer
The basis dimension is not the degrees of freedom	Intermediate	✓

Repeated measures in R

1 question.

Question	Level	Answer
A correlation four visits cannot have	Advanced	✓

Time series in R

1 question.

Question	Level	Answer
A holdout that keeps time in order	Advanced	✓

Checking a calculation

1 question.

Question	Level	Answer
Change one thing	Intermediate	✓

Bayesian statistics

133 questions in this part.

Bayesian foundations

15 questions.

Question	Level	Answer
Confidence procedures	Intermediate	–
What makes a hypothesis test?	Intermediate	–
One thousand posterior draws	Intermediate	–
Prediction is not estimation	Intermediate	–
The missing variance	Intermediate	–
Posterior mean under squared-error loss	Intermediate	✓
Confidence and credible intervals	Intermediate	✓
Equal-tailed and highest-density intervals	Intermediate	✓
Bayesian German tank problem	Intermediate	✓
Prior beliefs and conflicting data	Intermediate	✓
Interpreting identical interval endpoints	Intermediate	✓
Likelihood, prior and posterior	Intermediate	✓
Posterior prediction	Intermediate	✓
Two kinds of interval	Intermediate	✓
MAP and squared-error loss	Intermediate	✓

The Beta–Binomial model

11 questions.

Question	Level	Answer
The pseudo-count trap	Intermediate	–
Symmetry and context	Intermediate	–
A proper nonconjugate prior	Intermediate	–
Sequential updating	Intermediate	–
A future run of tosses	Intermediate	–
A geometric observation and a uniform prior	Intermediate	✓
A logit-normal prior for a coin	Intermediate	✓
Beta-Binomial conjugacy and prior influence	Intermediate	✓
Choosing a conjugate prior	Intermediate	✓
A nonconjugate prior and a change of variable	Intermediate	✓
Conjugacy	Intermediate	✓

Conjugate analysis for normal models

19 questions.

Question	Level	Answer
Four limiting checks	Intermediate	–
Where did the probability go?	Intermediate	–
Find the prior rather than recalling it	Intermediate	–
How many summaries?	Intermediate	–
Full conditionals	Intermediate	–
Normal–inverse-\chi^2 conjugacy	Intermediate	✓
Normal estimation and prediction	Intermediate	✓
Estimation and prediction	Intermediate	✓
Lognormal variance and conjugate inference	Intermediate	✓
Unknown Normal mean and variance: conditional versus marginal	Intermediate	✓
A Gibbs full conditional under independent priors	Intermediate	✓
Joint Normal conjugacy and exact sampling	Intermediate	✓
Normal mean, known variance	Intermediate	✓
Normal variance, known mean	Intermediate	✓
Normal mean and variance	Intermediate	✓
Jointly conjugate normal–inverse-gamma	Intermediate	✓
Lognormal variance	Intermediate	✓
Improper prior for a normal sample	Intermediate	✓
Gamma and inverse-Gamma kernels	Intermediate	✓

Markov chains, Gibbs sampling, and Metropolis–Hastings

31 questions.

Question	Level	Answer
Detailed balance	Advanced	–
A long run and a missed mode	Advanced	–
Posterior summaries with dependence	Advanced	–
Random-walk scale	Advanced	–
Adapt, discard, fix	Advanced	–
A bivariate-normal Gibbs sampler	Advanced	✓
Metropolis–Hastings for the logit-normal posterior	Advanced	✓
Random-walk Metropolis for a correlated normal	Advanced	✓
An independent Gamma proposal	Advanced	✓
Gibbs sampling from full conditionals	Advanced	✓
Random-walk Metropolis-Hastings	Advanced	✓
Gibbs sampling for a correlated normal target	Advanced	✓
Metropolis-Hastings with an asymmetric-proposal extension	Advanced	✓
Marginal and conditional distributions	Advanced	✓
Equilibrium and independence	Advanced	✓
Assessing a Metropolis–Hastings sampler	Advanced	✓
Gibbs, Metropolis–Hastings, and Monte Carlo error	Advanced	✓
General Beta–Binomial Gibbs sampler	Advanced	✓
Metropolis–Hastings with a Cauchy prior	Advanced	✓
Three-variable Gibbs sampling	Advanced	✓
Bayesian logistic regression	Advanced	✓
Gibbs sampling with a weighted count	Advanced	✓
Geometric–beta Gibbs sampler	Advanced	✓
Gibbs and random-walk Metropolis–Hastings	Advanced	✓
Binomial–beta Gibbs sampler	Advanced	✓
Mixed binomial–beta Gibbs sampler	Advanced	✓
Monte Carlo estimation	Advanced	✓
Markov property and invariance	Advanced	✓
Full conditionals and Gibbs	Advanced	✓
Metropolis–Hastings cancellations	Advanced	✓
Warm-up and dependence	Advanced	✓

Categorical data and the Dirichlet distribution

7 questions.

Question	Level	Answer
Beta hidden inside Dirichlet	Intermediate	–
Why not a multinomial prior?	Intermediate	–
Small concentrations	Intermediate	–
The simplex CLT	Intermediate	–
Dirichlet updating	Intermediate	–
Restaurant ordering methods	Intermediate	✓
Advertising responses and Dirichlet inference	Intermediate	✓

Bayesian hypotheses and model comparison

15 questions.

Question	Level	Answer
Who owns the boundary?	Advanced	–
Fruit posterior	Advanced	–
Probability is not action	Advanced	–
Make the simplex integral equal one	Advanced	–
Two routes to the same table	Advanced	–
An IQ threshold	Advanced	✓
Bayes factors and posterior odds	Advanced	✓
Evidence and posterior model probabilities	Advanced	✓
Comparing Exponential and Gamma lifetime models	Advanced	✓
Testing whether a coin is fair	Advanced	✓
Poisson flaws and posterior odds	Advanced	✓
Exponential versus gamma lifetimes	Advanced	✓
Battery lifetimes and a Bayes factor	Advanced	✓
Bayesian model selection	Advanced	✓
Evidence and model odds	Advanced	✓

Exponential families and conjugacy

18 questions.

Question	Level	Answer
Factorisation and data reduction	Advanced	–
A normal statistic	Advanced	–
Reading conjugacy from a kernel	Advanced	–
Three different “flat” Poisson priors	Advanced	–
Conjugacy is not guaranteed by a name	Advanced	–
Sufficiency and the posterior	Advanced	✓
Exponential observations parameterised by rate	Advanced	✓
Exponential observations parameterised by mean	Advanced	✓
Rayleigh conjugate prior	Advanced	✓
Gamma waiting times with an inverse-Gamma prior	Advanced	✓
Pareto likelihood and Gamma posterior	Advanced	✓
Machine downtime and a Gamma prior	Advanced	✓
Conjugate Bayesian inference for a Gamma rate	Advanced	✓
Beta downtime	Advanced	✓
Geometric success probability	Advanced	✓
Inverse-gamma waiting time	Advanced	✓
Sufficiency	Advanced	✓
Exponential family	Advanced	✓

Hierarchical Bayes

9 questions.

Question	Level	Answer
Pooling	Advanced	–
Derive the shrinkage weight	Advanced	–
Exchangeability is a scientific claim	Advanced	–
Two hyperpriors	Advanced	–
Sample from a grid	Advanced	–
Full Bayes and interval width	Advanced	–
Rat-tumour studies and hierarchical shrinkage	Advanced	✓
Hierarchical Poisson model	Advanced	✓
Pooling	Advanced	✓

Bayesian linear regression

8 questions.

Question	Level	Answer
Errors and residuals	Advanced	–
Normal before Student	Advanced	–
The inverse-Gamma shape trap	Advanced	–
Direct sampling or Gibbs?	Advanced	–
Mean response or new response?	Advanced	–
Independent and scaled priors	Advanced	–
Bayesian regression and prediction	Advanced	✓
Normal–inverse-\chi^2 regression	Advanced	✓

Generalised linear models

29 questions in this part.

Introduction to generalised linear models

9 questions.

Question	Level	Answer
Score, Hessian, and information identity	Intermediate	✓
Logistic regression and an adjusted effect	Intermediate	✓
Exponential regression and the score	Intermediate	✓
Negative-binomial canonical link	Intermediate	✓
The GLM components	Intermediate	✓
Links	Intermediate	✓
Score and information	Intermediate	✓
Fisher scoring and IRLS	Intermediate	✓
Logit, probit and odds	Intermediate	✓

Standard errors, and models for counts

7 questions.

Question	Level	Answer
Poisson regression model statement	Intermediate	✓
Interpreting Poisson regression coefficients	Intermediate	✓
Deriving the Poisson log-likelihood	Intermediate	✓
Poisson regression and overdispersion	Intermediate	✓
Poisson regression for fish species	Intermediate	✓
A log-link coefficient	Intermediate	✓
Negative-binomial variation	Intermediate	✓

Underdispersion, positive responses, and quasi-likelihood

6 questions.

Question	Level	Answer
Gamma regression from the exponential-family form	Intermediate	✓
Overdispersion and quasi-Poisson inference	Intermediate	✓
Gamma GLM for reaction times	Intermediate	✓
Positive continuous responses	Intermediate	✓
Quasilikelihood	Intermediate	✓
Dispersion	Intermediate	✓

Categorical responses

3 questions.

Question	Level	Answer
Multinomial logistic regression	Intermediate	✓
Categorical response types	Intermediate	✓
Proportional odds	Intermediate	✓

Paired comparisons, and how far a fit is from the data

4 questions.

Question	Level	Answer
Deviance and model adequacy	Intermediate	✓
Bradley–Terry	Intermediate	✓
Saturated model and deviance	Intermediate	✓
Significance is not adequacy	Intermediate	✓

Smoothing

7 questions in this part.

Smooth means

5 questions.

Question	Level	Answer
A binomial model with a smooth effect	Intermediate	✓
Changing from a logit to a probit link	Intermediate	✓
Cholesterol and heart disease	Intermediate	✓
Cubic splines and knots	Intermediate	✓
Roughness penalty	Intermediate	✓

Additive smooths

2 questions.

Question	Level	Answer
Testing and simplifying an additive model	Advanced	✓
GAMs and effective degrees of freedom	Advanced	✓

Statistical learning

144 questions in this part.

Covariance and the multivariate normal

8 questions.

Question	Level	Answer
Why a covariance is positive semi-definite	Intermediate	✓
Variances of linear combinations	Intermediate	✓
Uncorrelated but dependent	Intermediate	✓
Axes of a contour	Intermediate	✓
Normal marginals without joint normality	Intermediate	✓
The bivariate conditional	Intermediate	✓
A Schur-complement check	Intermediate	✓
Conditional normal prediction	Intermediate	✓

Estimation and inference for the multivariate normal

9 questions.

Question	Level	Answer
Where the n-1 comes from	Intermediate	✓
Pooling two groups	Intermediate	✓
Two factors of one covariance	Intermediate	✓
A determinant identity	Intermediate	✓
A small T^2 test	Intermediate	✓
A two-sample statistic	Intermediate	✓
Whitening and its limits	Intermediate	✓
Normal conditioning and whitening	Intermediate	✓
A transformation is not a distributional assumption	Intermediate	✓

Principal component analysis

7 questions.

Question	Level	Answer
A two-variable analysis	Intermediate	✓
Properties of the components	Intermediate	✓
The effect of correlation	Intermediate	✓
Principal components through the singular values	Intermediate	✓
How many components	Intermediate	✓
A low-variance predictor	Intermediate	✓
Principal components as a modelling step	Intermediate	✓

K-means clustering

8 questions.

Question	Level	Answer
Pairs and means	Intermediate	✓
Counting partitions	Intermediate	✓
K-means by hand	Intermediate	✓
A Voronoi boundary	Intermediate	✓
Reading the gap statistic	Intermediate	✓
The within-cluster sum cannot choose K	Intermediate	✓
What a K-means diagram must show	Intermediate	✓
Euclidean clusters and mixture components	Intermediate	✓

Mixtures and the EM algorithm

7 questions.

Question	Level	Answer
Mean and variance of a mixture	Intermediate	✓
An E step	Intermediate	✓
An M step	Intermediate	✓
An unbounded likelihood	Intermediate	✓
Counting parameters	Intermediate	✓
Label switching	Intermediate	✓
Mixtures versus K-means	Intermediate	✓

Model selection for stochastic models

7 questions.

Question	Level	Answer
Posterior odds	Intermediate	✓
BIC and AIC by hand	Intermediate	✓
The Laplace integral in one dimension	Intermediate	✓
KL divergence	Intermediate	✓
A tempting wrong turn	Intermediate	✓
Choosing model complexity	Intermediate	✓
Mixture selection and uncertainty	Intermediate	✓

Hierarchical clustering and kernel density estimation

6 questions.

Question	Level	Answer
Linkage by hand	Intermediate	✓
Number of merges	Intermediate	✓
Kernel density by hand	Intermediate	✓
A kernel is a density	Intermediate	✓
A tempting wrong turn	Intermediate	✓
Clustering and smoothing choices	Intermediate	✓

Statistical classifiers and discriminant analysis

8 questions.

Question	Level	Answer
A Bayes rule in one dimension	Intermediate	✓
Unequal costs	Intermediate	✓
LDA with unequal priors	Intermediate	✓
A quadratic boundary	Intermediate	✓
Parameter counts	Intermediate	✓
Fisher’s direction	Intermediate	✓
The fitted LDA model	Intermediate	✓
LDA and principal components	Intermediate	✓

Estimating error rates

7 questions.

Question	Level	Answer
A confusion matrix	Intermediate	✓
Test-set size	Intermediate	✓
The 0.632 rule	Intermediate	✓
Jackknife of the mean	Intermediate	✓
Costs of cross-validation	Intermediate	✓
A tempting wrong turn	Intermediate	✓
Separate tuning from evaluation	Intermediate	✓

Logistic regression

7 questions.

Question	Level	Answer
Derivative of the logistic function	Intermediate	✓
Odds ratios	Intermediate	✓
Linear discriminant analysis implies a logistic model	Intermediate	✓
Multinomial probabilities	Intermediate	✓
Complete separation	Intermediate	✓
Reading the deviance	Intermediate	✓
A logistic rule in an unfamiliar setting	Intermediate	✓

Nearest neighbours

8 questions.

Question	Level	Answer
Neighbours by hand	Intermediate	✓
Changing units	Intermediate	✓
Rank distance	Intermediate	✓
The factor of two	Intermediate	✓
A tempting wrong turn	Intermediate	✓
Normalisation and nearest neighbours	Intermediate	✓
Tuning a nearest-neighbour classifier	Intermediate	✓
What an accuracy table does and does not say	Intermediate	✓

Classification trees

7 questions.

Question	Level	Answer
Three impurities	Intermediate	✓
Which split is better?	Intermediate	✓
A tree by hand	Intermediate	✓
Affine invariance	Intermediate	✓
Penalised impurity	Intermediate	✓
A tempting wrong turn	Intermediate	✓
Decision trees and validation	Intermediate	✓

Ensembles, random forests, and boosting

7 questions.

Question	Level	Answer
The error decomposition	Advanced	✓
Variance of an average	Advanced	✓
Out-of-bag counts	Advanced	✓
One round of AdaBoost	Advanced	✓
The exponential-loss minimiser	Advanced	✓
A tempting wrong turn	Advanced	✓
Why an ensemble might improve a tree	Advanced	✓

Neural units

7 questions.

Question	Level	Answer
Derivative of the sigmoid	Advanced	✓
Logic gates	Advanced	✓
A decision boundary	Advanced	✓
Perceptron by hand	Advanced	✓
An XOR network of your own	Advanced	✓
Linear hidden units	Advanced	✓
Why XOR needs an extra layer	Advanced	✓

Backpropagation

7 questions.

Question	Level	Answer
Forward pass	Advanced	✓
A gradient by hand	Advanced	✓
Counting weights	Advanced	✓
Symmetric start	Advanced	✓
Delta form	Advanced	✓
Saturation	Advanced	✓
One backpropagation update	Advanced	✓

Networks in practice

7 questions.

Question	Level	Answer
Initial weights	Advanced	✓
Softmax gradient	Advanced	✓
Weight decay	Advanced	✓
Online versus batch	Advanced	✓
Sum of squares versus accuracy	Advanced	✓
Counting for NETtalk	Advanced	✓
Complexity and early stopping	Advanced	✓

Support vector machines

10 questions.

Question	Level	Answer
Distance to a hyperplane	Advanced	✓
A two-point machine	Advanced	✓
Which points matter?	Advanced	✓
Kernel as an inner product	Advanced	✓
A Gram matrix	Advanced	✓
Interpreting multipliers	Advanced	✓
A tempting wrong turn	Advanced	✓
Read the geometry	Advanced	✓
A unit-norm constraint	Advanced	✓
Nonlinear separation of XOR	Advanced	✓

High-dimensional analysis

9 questions.

Question	Level	Answer
Rank	Advanced	✓
Ridge makes the matrix invertible	Advanced	✓
A Bonferroni threshold	Advanced	✓
A step-up subtlety	Advanced	✓
Soft threshold	Advanced	✓
A tempting wrong turn	Advanced	✓
When ordinary linear discrimination is not defined	Advanced	✓
Principal components before linear discrimination	Advanced	✓
Selection in many dimensions	Advanced	✓

Graphical models

8 questions.

Question	Level	Answer
Cliques and separators	Advanced	✓
Precision to graph	Advanced	✓
A three-variable chain	Advanced	✓
Conditional independence from a partitioned covariance	Advanced	✓
How many graphs?	Advanced	✓
A tempting wrong turn	Advanced	✓
Read a Gaussian graphical model	Advanced	✓
Conditional association and sparsity	Advanced	✓

Correlated data

13 questions in this part.

Random intercepts

1 question.

Question	Level	Answer
Fixed and random effects	Advanced	✓

Random slopes, and a binary mixed model

6 questions.

Question	Level	Answer
A generalised linear mixed model	Advanced	✓
Interpreting a treatment–time interaction	Advanced	✓
Random slopes and changed conclusions	Advanced	✓
Toenail infection GLMM	Advanced	✓
Orthodontic growth curves	Advanced	✓
Random intercepts and slopes	Advanced	✓

Marginal models, and two responses at once

6 questions.

Question	Level	Answer
Conditional versus marginal dependence	Advanced	✓
Conditional versus marginal effects	Advanced	✓
Generalised estimating equations	Advanced	✓
Working correlation	Advanced	✓
Sandwich robustness	Advanced	✓
Vector-response regression	Advanced	✓

Time series

9 questions in this part.

Dependence along a series

7 questions.

Question	Level	Answer
Process and realisation	Advanced	✓
Two stationarity definitions	Advanced	✓
White noise is not necessarily independent	Advanced	✓
ACF and PACF	Advanced	✓
AR, MA and ARMA orders	Advanced	✓
Invertibility	Advanced	✓
ARCH and GARCH	Advanced	✓

Forecasting

2 questions.

Question	Level	Answer
Unit roots and ARIMA	Advanced	✓
Identification and residual checks	Advanced	✓