Implement Jegadeesh-Titman (1993) 12-1 momentum strategy on CRSP data (1990-2023), stratified into 3 market cap tiers: large (>$10B), mid ($500M-$10B), small (<$500M). Gross returns: large 0.
Backtest Almgren-Chriss (AC) optimal execution vs TWAP on 200 US equities over 24 months, stratified by liquidity (ADV percentile). Above 50th percentile ADV: AC outperforms TWAP by 3.
Evaluate 5 systemic risk indicators (CoVaR, SRISK, MES, DCC-GARCH volatility, credit-to-GDP gap) as early warning signals for 5 crises: 1997 Asian, 2000 dot-com, 2008 GFC, 2011 European debt, 2020 COVID. Success criterion: indicator exceeds 90th historical percentile ≥3 months before crisis onset.
Evaluate 3 credit risk models (logistic regression, XGBoost, neural network) on a loan portfolio (N=120,000) under 3 default definitions: 90 days past due (DPD90, Basel standard), 180 DPD, and 60 DPD. Model rankings change: at DPD90, XGBoost leads (AUC=0.
Simulate 10,000 return series from Student-t distributions (df=3,4,5,10,∞) at N=250,500,1000 trading days. Compute VaR at 99% using Gaussian assumption (deliberately misspecified for t-returns).
Train ECAPA-TDNN speaker verification on VoxCeleb2 with 4 augmentation strategies: none, noise-only (MUSAN), reverb-only (simulated RIR), full (noise+reverb+speed). Test on VOiCES corpus at 5 RT60 conditions (0.
Evaluate 3 segmentation models (nnU-Net, Swin-UNETR, TransUNet) on 4 organs (liver, kidney, pancreas, spleen) from Medical Segmentation Decathlon. Compute Dice, 95th-percentile Hausdorff Distance (HD95), Average Surface Distance (ASD), and Normalized Surface Dice (NSD).
Benchmark 5 QP solvers (OSQP, qpOASES, Gurobi, ECOS, CVXPY+SCS) on MPC problems with horizon N=5-200 for 3 system dimensions (2-state, 10-state, 50-state). Computation time t(N): theoretical O(N³) for dense QP.
Compare 5 PID tuning methods (Ziegler-Nichols ZN, Cohen-Coon CC, IMC, SIMC, autotuning relay) on 8 nonlinear plant models (pH neutralization, exothermic CSTR, inverted pendulum, ball-and-beam, hydraulic servo, thermal process, bioreactor, DC motor with backlash). Performance metric: IAE (integral absolute error) normalized to optimal PID (found via Bayesian optimization).
Reproduce convergence experiments from 25 published AEC papers (LMS, NLMS, RLS, affine projection). Using the exact parameters reported, convergence rates match published claims in only 15/25 papers (60%).
Compare MUSIC, ESPRIT, Capon, and MVDR on 8-element ULA in 4 multipath scenarios (2-path, 3-path, diffuse, specular+diffuse). At SNR≥10dB: all methods agree within 0.
Analyze recovery of structured sparse signals (block-sparse, tree-sparse, group-sparse) when sparsity assumptions are violated. Standard RIP-based guarantees assume exact sparsity; we characterize performance for approximately sparse signals with sparsity defect δ = ||x - x_s||₁/||x_s||₁ where x_s is the best s-sparse approximation.
Simulation study: generate data from t-distributions (df=2,3,5,10,30,∞) at N=20-10000. Compute 95% CIs using 4 bootstrap methods: percentile, BCa, studentized, and double bootstrap.
Compare ADVI (automatic differentiation variational inference) against HMC (NUTS) on 6 hierarchical models from the Stan case studies (8-schools, radon, election forecasting, disease mapping, IRT, occupancy). ADVI posterior means match HMC within 3% (mean absolute deviation).
Re-run 80 published Bayesian ecology models from 4 journals (Ecology, Ecological Applications, Methods in Ecology and Evolution, Journal of Animal Ecology). Apply 4 convergence diagnostics: R-hat (<1.
Compare 8 popular power calculators (G*Power, PASS, R pwr package, Stata power, nQuery, PS, ClinCalc, SampleSize4ClinicalTrials) on clustered designs (ICC=0.01-0.
Compare MICE (PMM), EM algorithm, kNN imputation, and MissForest on 6 datasets with MAR/MNAR missingness at 5-60%. Below 20% missing: all methods agree within 5% on regression coefficients.
Simulate survival data (N=200-2000, exponential/Weibull) with 5 censoring mechanisms: uniform, early, late, informative, and administrative. Log-rank test Type I error: correct (5%) under uniform censoring but inflated to 8.
Simulate 100,000 A/B tests at N=100-100000 per arm with true effect sizes from δ=0 to δ=0.3.
Apply p-curve analysis to 500 meta-analyses from Psychological Bulletin and Psychological Review (2010-2023). Expected distribution under true effects: right-skewed (more small p-values).