11 Facts About Statistical inference

Statistical inference is the process of using data analysis to infer properties of an underlying distribution of probability.

Statistical inference makes propositions about a population, using data drawn from the population with some form of sampling.

In Bayesian Statistical inference, randomization is of importance: in survey sampling, use of sampling without replacement ensures the exchangeability of the sample with the population; in randomized experiments, randomization warrants a missing at random assumption for covariate information.

One interpretation of frequentist Statistical inference is that it is applicable only in terms of frequency probability; that is, in terms of repeated sampling from a population.

In particular, frequentist developments of optimal Statistical inference make use of loss functions, which play the role of utility functions.

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Bayesian inference uses the available posterior beliefs as the basis for making statistical propositions.

Formally, Bayesian Statistical inference is calibrated with reference to an explicitly stated utility, or loss function; the 'Bayes rule' is the one which maximizes expected utility, averaged over the posterior uncertainty.

Some likelihoodists reject Statistical inference, considering statistics as only computing support from evidence.

Fiducial inference was an approach to statistical inference based on fiducial probability, known as a "fiducial distribution".

Fraser developed a general theory for structural Statistical inference based on group theory and applied this to linear models.

Predictive inference is an approach to statistical inference that emphasizes the prediction of future observations based on past observations.