Predicting loan default from demographic and financial indicators is a calibration problem as much as a classification one. A model that maximises accuracy on an imbalanced outcome is useless if its predicted probabilities are poorly calibrated, since lending decisions depend on probability estimates, not hard labels. The dataset also carries multicollinear features and meaningful missingness that cannot be listwise-deleted without biasing the training set.

KNN imputation preserves the joint feature distribution before any reduction step. Sparse PCA and standard PCA are both evaluated as pre-processing stages to assess whether sparsity-inducing constraints improve out-of-sample separation. Three model families are then fitted independently: a multi-layer perceptron, Random Forest via ranger, and XGBoost. Hyperparameter search uses Racing ANOVA to discard poor configurations early, followed by Bayesian optimisation on the survivors. All tuning is done inside a cross-validation loop with no information leakage.

Models compared on ROC-AUC, F1, Brier Score, and Precision-Recall curves across folds to separate discrimination from calibration. XGBoost with SPCA pre-processing produced the best Brier Score, indicating well-calibrated default probabilities in addition to strong separation. Feature importance analysis confirmed that repayment history and debt-to-income ratio drove predictions across all three model families.

Fine needle aspirate images of breast masses yield 30 digitised nucleus measurements per biopsy, covering radius, texture, perimeter, area, smoothness, compactness, concavity, concave point count, symmetry, and fractal dimension, each summarised as mean, standard error, and worst-case value. The resulting feature space is severely collinear: the first two PCA components capture 63% of variance, so any model that treats all 30 predictors as independent will inflate its apparent importance scores without actually improving separation. The dataset is also class imbalanced at roughly 37% malignant, which inflates accuracy while masking sensitivity failures.

Boruta wrapper selection identifies features that genuinely contribute against a shadow-feature baseline, removing confirmed noise predictors before modelling. PCA biplots via factoextra confirm which nucleus measurements drive the malignant versus benign axis. SMOTE oversampling corrects class imbalance at the recipe stage inside the cross-validation fold, with no leakage into the assessment set. Eight model families are then compared under a single tidymodels workflow: Logistic Regression, Random Forest, SVM-RBF, XGBoost, BART, Naive Bayes, KNN, and a Decision Tree. Racing ANOVA prunes unpromising hyperparameter configs early; Bayesian optimisation refines the survivors. Calibration is assessed with betacal alongside the standard discrimination metrics.

SVM-RBF and XGBoost produced the strongest separation across cross-validated ROC-AUC and F1. Boruta confirmed that worst-case concavity, concave point count, and perimeter were the three most stable predictors across resampling folds, consistent with the pathological signature of irregular nuclear edges in malignant tissue. Hierarchical clustering on the PCA-reduced space recovers the malignant versus benign partition without any labels, confirming that the morphological signal is strong enough to be unsupervised.

Did a policy or intervention actually change a time series outcome, or was the change explained by pre-existing trend and seasonality? Causal inference on observational time series with a single treated unit.

BSTS decomposes the series into trend, seasonality, and regression components, each with a full posterior distribution producing uncertainty bands rather than point estimates. INLA handles posterior computation via Laplace approximations, substantially faster than MCMC. Causal identification uses an interrupted time series design: fit pre-intervention, project forward counterfactually, compare to observed. Key assumption: parallel trends in the absence of intervention.

Models time-to-event data where many observations are censored. Handles competing risks and time-varying covariates with full posterior uncertainty.

Fully Bayesian hierarchical survival models. Priors on the baseline hazard encode genuine uncertainty about the underlying time-to-event distribution. Competing risks are modelled via cause-specific hazards rather than collapsed into a single endpoint. The hierarchical component pools information across subgroups while allowing each its own parameters. Right-censoring is assumed non-informative.