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Concept
Interval estimation
Summary
In statistics, interval estimation is the use of sample data to estimate an interval of possible values of a parameter of interest. This is in contrast to point estimation, which gives a single value.
The most prevalent forms of interval estimation are confidence intervals (a frequentist method) and credible intervals (a Bayesian method);
less common forms include likelihood intervals and fiducial intervals.
Other forms of statistical intervals include tolerance intervals (covering a proportion of a sampled population) and prediction intervals (an estimate of a future observation, used mainly in regression analysis).
Non-statistical methods that can lead to interval estimates include fuzzy logic.
Tolerance interval#Relation to other intervalsConfidence interval#Alternatives and critiques and Prediction interval#Contrast with parametric confidence intervals
The scientific problems associated with interval estimation may be summarised as follows:
When interval estimates are reported, they should have a commonly held interpretation in the scientific community and more widely. In this regard, credible intervals are held to be most readily understood by the general public. Interval estimates derived from fuzzy logic have much more application-specific meanings.
For commonly occurring situations there should be sets of standard procedures that can be used, subject to the checking and validity of any required assumptions. This applies for both confidence intervals and credible intervals.
For more novel situations there should be guidance on how interval estimates can be formulated. In this regard confidence intervals and credible intervals have a similar standing but there are differences:
credible intervals can readily deal with prior information, while confidence intervals cannot.
confidence intervals are more flexible and can be used practically in more situations than credible intervals: one area where credible intervals suffer in comparison is in dealing with non-parametric models (see non-parametric statistics).
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