Inference

Inference is the process of drawing conclusions from evidence or premises. It encompasses formal, rule-based reasoning as well as informal, data-driven judgment and is central to science, philosophy, law, and computer science.

In logic, inference concerns conclusions that must follow from given premises (deductive inference). Common forms include modus ponens and modus tollens. Inductive inference generalizes from observed cases to broader generalizations and is inherently probabilistic. Abductive inference seeks the most plausible explanation for available evidence and is common in medicine and detective work.

Statistical inference uses data to draw conclusions about larger populations. It includes estimation of parameters, hypothesis testing, and the construction of confidence or credible intervals. Bayesian inference combines prior beliefs with data via Bayes' rule to produce posterior distributions, while frequentist methods emphasize long-run error rates and confidence statements.

In machine learning and artificial intelligence, inference commonly means applying a trained model to new data to produce predictions or decisions, as distinct from the training process that learns model parameters.

Limitations of inference include uncertainty, dependency on model assumptions, potential biases in data, and the danger of conflating correlation with causation. Good inference relies on transparent methods, explicit assumptions, and careful consideration of alternatives.