Maximum Posterior Probability Estimators of Map Accuracy

Assessing the accuracy of land cover maps is often prohibitively expensive because of the difficulty of collecting a statistically valid probability sample from the classified map. Even when post-classification sampling is undertaken, cost and accessibility constraints may result in imprecise estimates of map accuracy. If the map is constructed via supervised classification, then the training sample provides a potential alternative source of data for accuracy assessment. Yet unless the training sample is collected by probability sampling, the estimates are, at best, of uncertain quality, and may be substantially biased. In this article, a new approach to map accuracy assessment based on maximum posterior probability estimators is discussed. These estimators may be used to reduce bias and increase precision when the training sample is collected without benefit of probability sampling, and also to increase precision of estimates obtained from post-classification sampling. A calibrated maximum posterior probability estimate of map accuracy is computed by first estimating the probability that each map unit has been correctly classified. Then, the map unit estimates are calibrated using a function derived from either the training sample or a post-classification sample. Finally, estimates of map accuracy are computed as means of the calibrated map unit estimates. In addition to discussing maximum posterior probability estimators, this article reports on a simulation study comparing three approaches to estimating map accuracy: 1) post-classification sampling, 2) resampling the training sample via cross-validation, and 3) maximum posterior probability estimation. The simulation study showed substantial reductions in bias and improvements in precision when comparing calibrated maximum posterior probability and cross-validation estimators when the training sample was not representative of the map. In addition, combining an ordinary post-classification estimator and the maximum posterior probability estimator produced an estimator that was at least, and usually more precise than the ordinary post-classification estimator.