Statistical inference is the process of drawing conclusions about a population or data-generating process from a finite sample, while quantifying the uncertainty of those conclusions. It encompasses estimation of parameters, hypothesis testing and prediction, grounded in probability theory. Both frequentist and Bayesian frameworks provide formal machinery for reasoning under sampling variability, underpinning model evaluation in machine learning.
Overview
- Inference treats observed data as one realisation of a random process and asks what the underlying parameters or future outcomes are likely to be.
- Estimators summarise the sample; confidence or credible intervals express how much that summary may vary.
- Hypothesis tests and predictive distributions translate uncertainty into decisions, forming the statistical backbone of empirical machine learning.
Mechanisms
- Point and interval estimation of population parameters.
- Hypothesis testing controlling error rates under sampling variability.
- Bayesian updating of prior beliefs with observed evidence.
- Predictive inference and generalisation bounds for unseen data.
Applications
- Validating model performance through cross-validation and significance testing.
- Estimating effect sizes and uncertainty in scientific experiments.
- Calibrating probabilistic forecasts and risk models.