Statistics is the language with which claims are tested and uncertainty is communicated. Exploratory analysis generates hypotheses from the data; confirmatory analysis then tests them with formal procedures. Hypothesis testing evaluates a claim about a population by computing a p-value, the probability of observing data at least as extreme as what was measured, assuming the null hypothesis is true. A result is declared statistically significant when this probability is below a chosen threshold, typically 0.05. Bootstrapping, resampling with replacement, provides an alternative route to the same kind of inference: it builds an empirical sampling distribution from the data itself, from which confidence intervals are read. A confidence interval is a range that, under repeated sampling, contains the true parameter with a stated frequency — a frequentist interpretation that contrasts with the Bayesian view, where probability reflects updated beliefs given priors and observed data via Bayes' theorem.
Correlation quantifies a linear association between variables; causation asserts that one variable influences another. The distinction is critical, because correlation does not imply causation: confounding variables that affect both predictor and outcome can produce spurious relationships. Simpson's paradox dramatizes the point — a trend that holds for the population can reverse when the data is split into groups. Careful study design and adjustment for confounders are the usual defenses.
As models grow more complex, interpretability becomes essential. Model interpretability is the degree to which a human can understand a model's decisions. SHAP (SHapley Additive exPlanations) attributes a prediction to features using game-theoretic Shapley values, giving a consistent, locally accurate explanation. LIME (Local Interpretable Model-agnostic Explanations) approximates the model locally with an interpretable surrogate to explain individual predictions. Permutation importance offers a more global view: shuffle a feature and observe how much performance drops, capturing reliance on that feature. These tools help practitioners debug models, build trust with stakeholders, and satisfy regulatory or ethical review.
Fairness in machine learning asks whether models systematically disadvantage protected groups. Bias in data — historical skews, underrepresentation, label noise that correlates with identity — can flow into models as disparate outcomes. Quantitative criteria formalize the goal: demographic parity asks for similar outcome rates across groups, while equalized odds asks for equal true positive and false positive rates across groups. These criteria can be in tension with each other and with accuracy, so choices must be deliberate and documented. Privacy-preserving methods like differential privacy add calibrated noise so that an individual's data does not significantly affect the output, and federated learning trains models on decentralized devices without centralizing raw data, reducing exposure risk while still producing useful models.