In statistics, interval estimation is the use of sample data to estimate an interval of possible values of a (sample) 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, fiducial intervals, tolerance intervals, and prediction intervals. For a non-statistical method, interval estimates can be deduced from fuzzy logic.

Confidence intervals are used to estimate the parameter of interest from a sampled data set, commonly the mean or standard deviation. A confidence interval states there is a 100γ% confidence that the parameter of interest is within a lower and upper bound. A common misconception of confidence intervals is 100γ% of the data set fits within or above/below the bounds, this is referred to as a tolerance interval, which is discussed below.

There are multiple methods used to build a confidence interval, the correct choice depends on the data being analyzed. For a normal distribution with a known variance, one uses the z-table to create an interval where a confidence level of 100γ% can be obtained centered around the sample mean from a data set of n measurements, . For a Binomial distribution, confidence intervals can be approximated using the Wald Approximate Method, Jeffreys interval, and Clopper-Pearson interval. The Jeffrey method can also be used to approximate intervals for a Poisson distribution. If the underlying distribution is unknown, one can utilize bootstrapping to create bounds about the median of the data set.

As opposed to a confidence interval, a credible interval requires a prior assumption, modifying the assumption utilizing a Bayes factor, and determining a posterior distribution. Utilizing the posterior distribution, one can determine a 100γ% probability the parameter of interest is included, as opposed to the confidence interval where one can be 100γ% confident that an estimate is included within an interval.

$${\displaystyle {\text{Posterior}}\ \propto \ {\text{Likelihood}}\times {\text{Prior}}}$$

While a prior assumption is helpful towards providing more data towards building an interval, it removes the objectivity of a confidence interval. A prior will be used to inform a posterior, if unchallenged this prior can lead to incorrect predictions.

The credible interval's bounds are variable, unlike the confidence interval. There are multiple methods to determine where the correct upper and lower limits should be located. Common techniques to adjust the bounds of the interval include highest posterior density interval (HPDI), equal-tailed interval, or choosing the center the interval around the mean.