Statistical Inference
- Quantify the strength of inductive inferences from facts, in the form of data (\( D \)), and other premises, e.g. models, to hypotheses about the phenomena producing the data.
- Quantify via probabilities, or averages calculated using probabilities. Frequentists (\( \mathcal{F} \)) and Bayesians (\( \mathcal{B} \)) use probabilities very differently for this.
- To the pioneers such as Bernoulli, Bayes and Laplace, a probability represented a degree-of-belief or plausability: how much they thought that something as true based on the evidence at hand. This is the Bayesian approach.
- To the 19th century scholars, this seemed too vague and subjective. They redefined probability as the long run relative frequency with which an event occurred, given (infinitely) many repeated (experimental) trials.