STAT5003 Cheatsheet · Computational Statistical Methods

01 · Exam mapcourse.json + final FAQ

“Cheat sheet: One A4 sheet of handwritten notes double-sided. It should be handwritten!! Please note that printed sheets, including those written on the iPad and printed, are not allowed” (STAT5003 Final Exam FAQ, Semester 2 2026)

02 · Response spineC1 · C12

three-error audittranslation error → calculation error → interpretation error.
Repair the first failed move; then recheck a limit or independent route.

Exam use Read the task verb first: estimate, predict, classify, compare, diagnose or interpret. Keep observed inputs separate from derived quantities.

03 · Regression & smoothersC3 · course overview

linear modelE(Y|X)=β₀+β₁X₁+⋯+βₚXₚ
ŷᵢ=β̂₀+Σⱼβ̂ⱼxᵢⱼ · eᵢ=yᵢ−ŷᵢ

Coefficient: expected change in the conditional mean for one-unit increase in that predictor, holding the others constant, under stated assumptions. Prediction belongs within the modelled range; attach uncertainty and units. Association from a fitted model is not automatically causal.

bias–variance decompositionExpected prediction error = irreducible noise + Bias² + Variance.

Output stem “Holding the other modelled predictors constant, the fitted conditional mean changes by … per …; this is an association within the model and data range.”

04 · Density & likelihoodC4 · glossary

kernel density estimatef̂ₕ(x)=(1/nh)ΣᵢK((x−xᵢ)/h)
small h → less smoothing · large h → more smoothing

05 · Classification coreC5 · glossary

kNN: classify from nearby labelled cases. Scale predictors first or a large-unit variable dominates distance. Small neighbourhoods are flexible and sample-sensitive; larger neighbourhoods smooth the boundary. Tune inside resampling, then assess on independent evidence.

confusion metricsAccuracy=(TP+TN)/N
Sensitivity/recall=TP/(TP+FN)
Specificity=TN/(TN+FP)
Precision=TP/(TP+FP)

Metric choice: actual positives → sensitivity; actual negatives → specificity; positive calls → precision. Under class imbalance, inspect errors by actual and predicted class rather than reporting accuracy alone.

06 · SVM + missing dataC6 · glossary

08 · CV & model selectionC7 · glossary

k-fold estimateCV error = (1/k)Σⱼ Loss on fold j, after fitting on the other folds.

Split roles: training fits parameters; validation compares or tunes choices; independent test evidence supports the final out-of-sample claim. Once you repeatedly tune to one validation result, it has become training information.

09 · Regularisationglossary

ridgeminβ Loss(β)+λΣⱼβⱼ²
lassominβ Loss(β)+λΣⱼ|βⱼ|

λ controls shrinkage. Ridge shrinks correlated coefficients; lasso can set coefficients exactly to zero. Tune λ inside the resampling scheme and report the performance estimate from evidence not used to choose it.

10 · Trees & ensemblesC8 · overview

Boundary Predictive importance is model- and metric-dependent. Never turn a ranking into a causal effect.

11 · BootstrapC9

1. Define the observed empirical data and target statistic.
2. Resample according to the design; recompute the statistic each time.
3. Use the bootstrap distribution for uncertainty or interval construction.
4. State dependence, sampling and bias limitations.

A bootstrap inherits bias and dependence problems in the observed sample. Naive row resampling is not justified merely because software makes it easy; match the resampling unit to the data structure.

12 · Output sentenceC12

13 · Monte CarloC10 · overview

Monte Carlo meanμ̂ᴹᶜ=(1/M)Σₘg(Xₘ)
Monte Carlo SE ≈ s[g(X)]/√M

Define the target and sampling mechanism; simulate reproducibly; compute the estimator; report simulation error. Increasing iterations shrinks simulation error at roughly the square-root rate. It does not repair biased inputs or model misspecification.

14 · Bayes & MCMCC11 · overview

Bayes rule, proportional formp(θ|y) ∝ p(y|θ)p(θ)
posterior ∝ likelihood × prior

Trap A long chain is not evidence of convergence or adequate mixing. More draws cannot rescue the wrong target or an unidentified model.

D1 · Regression response [4]C3 worked example

Prompt pattern: translate coefficient output into a conditional prediction and uncertainty statement; restore the missing link between the linear model and residual diagnostics.

1. [1] Mark the starting condition or object represented by the linear model.
2. [1] Write the change, rule or mechanism supplied by prediction as a verb-led link.
3. [1] Show how that link reaches residual diagnostics; do not skip an intermediate quantity or stage.
4. [1] Answer with the completed chain and preserve the limit: association from a fitted model is not automatically causal.

answer frameFor [population], holding [other predictors] constant, [coefficient/prediction] means … . The residual check shows … . This supports [narrow conclusion], subject to [assumption/range/uncertainty]; it is not automatically causal.

R3 · Drill protocolstudy strategy

D2 · Classification response [4]C5 worked example

Prompt pattern: connect a classification threshold to errors and stakeholder cost; keep classification rule, distance/scaling and confusion matrix separate.

1. [1] State the exact comparison required.
2. [1] Define the classification rule and attach the observation that belongs to it.
3. [1] Define distance and scaling separately; state why the concepts cannot be collapsed.
4. [1] Apply the confusion matrix to the same evidence and conclude within the limit that accuracy alone can mislead under class imbalance.

answer frameThe rule classifies … at threshold … . Scaling matters because … . The confusion matrix shows [error type/metric]; given stakeholder cost, choose … rather than relying on accuracy alone.

D3 · Cross-validation [4]C7 worked example

Prompt pattern: estimate out-of-sample performance without leaking validation information; use k-fold CV and tuning bias to test the choice.

1. [1] Extract the outcome or operation the task requires.
2. [1] State the precondition under which training/validation is relevant.
3. [1] Use k-fold CV to reject the nearest alternative; run a failure-path check for tuning bias.
4. [1] Choose the response and state when it must be withdrawn: repeated tuning against one validation result makes it part of training.

Fast check For every transformation ask: “Was this fitted using only the training portion available at that stage?”

D4 · Bootstrap response [4]C9 worked example

Prompt pattern: approximate sampling uncertainty from a reproducible resampling scheme; assign empirical resampling, bootstrap distribution and interval construction separate jobs.

1. [1] Use empirical resampling to fix the object or condition being analysed.
2. [1] Use the bootstrap distribution to state the mechanism.
3. [1] Use interval construction for a consequence, counter-case or check.
4. [1] Conclude without crossing the limit that the bootstrap inherits bias and dependence problems in the observed sample.

answer frameResample [unit] from the observed empirical data under [scheme]; recompute [statistic] each time. The bootstrap distribution approximates sampling uncertainty, giving [interval/SE]. This relies on [sampling/dependence condition].

D5 · Monte Carlo + MCMC [4]C10–C11 worked patterns

Monte Carlo prompt: quantify approximation error and improve efficiency without changing the target. MCMC prompt: separate posterior updating from the computation used to approximate it.

1. [1] Define the target quantity represented by the Monte Carlo estimator.
2. [1] Write the simulation-error relationship before substituting or simplifying.
3. [1] Carry the computation through; use variance reduction as the interpretation check.
4. [1] Report result, unit and scope; preserve the model-misspecification boundary.

Square-root recall Multiplying iterations substantially gives only square-root improvement in Monte Carlo error; do not confuse computational precision with model validity.

R1 · Method choosercourse overview

R2 · Trap registerC2–C12 limits