Abstract Digital imagery and remote sensing have become popular and accessible tools in many scientiic research ields. Accuracy of classiication, the degree of agreement between classiication and ground truth, is traditionally quantiied by an error matrix and summarized using agreement measures such as Cohen’s kappa. he kappa statistic, however, can be shown to be a transformation of the marginal proportions commonly referred to as omissional and commissional error rates. Alternative estimation methods for these agreement measures include binomial, bootstrap and Bayesian techniques. In this study, we develop a Bayesian estimation method for omissional and commissional errors and discuss its utilization in variability assessment and inference. We will also show how additional or sequential information may be incorporated to improve the estimation situation. Techniques are demonstrated using previously published data. Application of Bayesian Methods for Assessing Detection Accuracy in Remote Sensing Publication History: Received: June 10, 2016 Accepted: August 04, 2016 Published: August 06, 2016 Keywords: Bayesian estimation, Agreement measures, Error rates Research Article Open Access Introduction In remote sensing, accuracy of classiication is traditionally assessed by the comparison of classiied pixels with ground truth using agreement measures such as Cohen’s kappa. Conventionally, statistical inferences concerning the agreement measures have been based on asymptotic normality assumptions. While asymptotic methods may produce satisfactory results in certain instances, they fail to account for the underlying distribution of the classiied data. his can result in poor and inconsistent inferences regarding the classiication accuracy. Accuracy of classiication is oten represented in the form of an error matrix [1, 2]. he rows of this table (i=1, 2, 3, ..., C) represent the computer or human generated classiication and the columns (j=1, 2, 3, ..., C) denote the reference or ground truth categories: where, x ii is the number of pixels correctly classiied in category i, N i. and N .i are the corresponding marginal totals for classiication and ground truth, respectively, and N = ΣN i. = ΣN .i . Various methods have been suggested for assessing the degree of ground truth agreement for each category. Common measures include conditional kappa, a general index of agreement [3]: , the omissional error rate, measuring the proportion of pixels incorrectly omitted from a classiication: , * Corresponding Author: Dr. Bahman Shaii, Statistical Programs, P.O. Box 442337, University of Idaho, Moscow, ID, 83844-2337 USA, E-mail: bshaii@uidaho.edu Citation: Shaii B, Price WJ (2016) Application of Bayesian Methods for Assessing Detection Accuracy in Remote Sensing. Int J Appl Exp Math 1: 106. doi: http://dx.doi.org/10.15344/ijaem/2016/106 Copyright: © 2016 Shaii et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. International Journal of Applied & Experimental Mathematics Bahman Shaii* and William J. Price Statistical Programs, P.O. Box 442337, University of Idaho, Moscow, ID, 83844-2337, USA Int J Appl Exp Math IJAEM, an open access journal Volume 1. 2016. 106 Shaii et al., Int J Appl Exp Math 2016, 1: 106 http://dx.doi.org/10.15344/ijaem/2016/106 and the commissional error rate, measuring the proportion of pixels erroneously committed to a classiication category [4]: , where x ii ⁄ N .i and x ii ⁄ N i. are commonly referred to as producer’s and user’s accuracies [5]. he kappa statistic has been suggested as a means of assessing the degree of agreement in remotely sensed data because it equally weighs both omissional and commissional errors [6]. Remote sensing, however, presents a unique situation for conditional kappa in which, for a given image classiication, the marginal ground truth totals, N .i , as well as classiied totals for each class, N i. , are constant. Under these conditions, (1) becomes a simple monotonic function of the omissional error rate [7]. It should also be noted that, although kappa treats misclassiications equally, in many cases it may be important to distinguish between the error types [8]. For these reasons, it will be more advantageous to carry out accuracy assessment based on the later two measures, namely O l and O l Using Bayesian estimation and maximum entropy, Shaii et al, [9] developed a methodology that may be used for estimation and inference regarding the aforementioned agreement measures. Furthermore, it has been shown that the Bayesian estimation technique is superior to that of the exact binomial, and that due to its ability to incorporate prior information, it can be more advantageous than the parametric bootstrapping technique [10]. In this paper, we review the Bayesian estimation technique for omissional and commissional error rates and illustrate its inferential use for image variability assessment and comparison. Furthermore, 1 2 3 ... C 1 x11 x12 x13 ... x 1c N1. 2 x21 x22 x23 ... x 2c N2. 3 x31 x32 x33 ... x 3c N3. C xc1 xc2 xc3 ... xcc NC. N.1 N.2 N.3 ... N.C N ... ... ... ... ... ... ... Ground Truth ˆ . O 1 ii l i x N = − ˆ ˆ . . . 1 ii i i l i x N N N N N κ   −     =   −     ˆ . C 1 ii l i x N = − ˆ