Interval estimation
In statistics, interval estimation is the use of sample data to calculate an interval of possible values of an unknown population parameter; this is in contrast to point estimation, which gives a single value. Jerzy Neyman identified interval estimation as distinct from point estimation. In doing so, he recognized that then-recent work quoting results in the form of an estimate plus-or-minus a standard deviation indicated that interval estimation was actually the problem statisticians really had in mind.
The most prevalent forms of interval estimation are:
Other forms include:
Other forms of statistical intervals, which do not estimate parameters, include:
Non-statistical methods that can lead to interval estimates include fuzzy logic. An interval estimate is one type of outcome of a statistical analysis. Some other types of outcome are point estimates and decisions.Discussion
The scientific problems associated with interval estimation may be summarised as follows:
Severini discusses conditions under which credible intervals and confidence intervals will produce similar results, and also discusses both the coverage probabilities of credible intervals and the posterior probabilities associated with confidence intervals.
In decision theory, which is a common approach to and justification for Bayesian statistics, interval estimation is not of direct interest. The outcome is a decision, not an interval estimate, and thus Bayesian decision theorists use a Bayes action: they minimize expected loss of a loss function with respect to the entire posterior distribution, not a specific interval.
