Confidence Intervals for Forecast Verification

The manuscript is an attempt to present in a single document the various types of confidence intervals, their assumptions, and other issues as they pertain to forecast verification applications. Confidence intervals can be categorized into parametric and nonparametric intervals. The most common parametric intervals are those based on the assumption of approximate normality. Such intervals are discussed in detail for those verification statistics that use this approximation, in addition to details about the assumptions involved and how to check and account for the assumptions. Bootstrap intervals are also discussed. Of particular importance are the assumptions underlying the bootstrap procedure, which are frequently overlooked because of a miscommunication that the procedure has no assumptions. When the assumptions are met, or they are accounted for within the bootstrap procedure, then this approach can provide highly accurate intervals for most statistics of interest. The various bootstrap confidence intervals (along with their pros and cons) and bootstrap methods are described.