**Coverage probability**is the probability a procedure for the construction of a region will give an interval that covers (contains) the true population parameter. In other words, it is the chance a constructed interval contains the parameter you’re interested in [1].

## The Ideal Coverage Probability

Coverage probability is a way to evaluate the performance of a confidence interval estimator; ideally, your CI should have the highest possible coverage probability [2]. **The usual way to choose a coverage probability is by convention or your best judgment**, with 90%, 95%, and 99% being typical choices [3]. However, this isn’t easy: larger prediction intervals (e.g., 95%) might contain all of your values, but these tend to be very wide prediction intervals with little practical value. Setting a too-narrow interval may result in all of your values falling outside the interval, which again is not practical. The goal then, is to find the middle ground.

## Coverage Probability vs. Confidence Level

At first glance, coverage probability looks exactly the same as confidence level. However, there are several differences [4]:

- Coverage probability is the probability an interval surrounding the unknown parameter depends on the unknown parameter value; Confidence is the infimum of all coverage probabilities.
- While confidence levels can be calculated by hand, coverage probability is best calculated by computer, as this involves finding the sum of infinite calculations.
- Coverage probabilities tend to be higher than confidence levels if approximations are used to create confidence intervals; Coverage and confidence
*can*be equal when working with continuous distributions (for example, if you’re constructing an interval for the mean of a normally distributed population with a t-distribution [5]); they are never equal when dealing with discrete distributions (for example, when constructing binomial confidence intervals).

## References

[1] Lecture 5: Confidence Intervals. Retrieved February 6, 2021 from: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.431.5273&rep=rep1&type=pdf

[2] Harvil, J. (2021). Size and Coverage Probability. Retrieved February 6, 2021 from: https://mediaspace.baylor.edu/media/Size+and+Coverage+Probability/1_u4x1f923/193100023

[3] Landon, J. & Singpurwalla, N. Statistical Practice: Choosing a Coverage Probability for Prediction Intervals.

[4] Cook, P. Coverage vs. Confidence. Retrieved February 6, 2021 from: https://www.mathematica-journal.com/2021/03/03/coverage-versus-confidence/

[5] Meyer, M. (2019). Probability and Mathematical Statistics Theory, Applications, and Practice in R. Society for Industrial and Applied Mathematics.