Calibration of a Confidence Interval for a Classification Accuracy

Abstract

Coverage of nominal 95% confidence intervals of a proportion estimated from a sample obtained under a complex survey design, or a proportion estimated from a ratio of two random variables, can depart significantly from its target. Effective calibration methods exist for intervals for a proportion derived from a single binary study variable, but not for estimates of thematic classification accuracy. To promote a calibration of confidence intervals within the context of land-cover mapping, this study first illustrates a common problem of under and over-coverage with standard confidence intervals, and then proposes a simple and fast calibration that more often than not will improve coverage. The demonstration is with simulated sampling from a classified map with four classes, and a reference class known for every unit in a population of 160,000 units arranged in a square array. The simulations include four common probability sampling designs for accuracy assessment, and three sample sizes. Statistically significant over- and under-coverage was present in estimates of user’s (UA) and producer’s accuracy (PA) as well as in estimates of class area proportion. A calibration with Bayes intervals for UA and PA was most efficient with smaller sample sizes and two cluster sampling designs.