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The purpose of this paper is to establish a direct method for assessing the confidence in the detection and identification probabilities for segmented observations that are not identically distributed across assigned segments within a region. This paper arrives at easily computable confidence intervals by showing through mathematical analysis that: I. The probability of successful detection within each test segment can be characterized by a Beta distribution; II. The distribution of a weighted sum of independent but non-identically distributed sample means is asymptotically Normally distributed by the Lyapunov variant of the Central Limit Theorem, i.e., the approximation improves as the number of samples increases; III. Given that the distribution of the sample means convergences to a Normal distribution, the confidence intervals about the observed sample means for both the detection and identification probabilities can be determined in closed form for multiple target types. The motivation for this approach is the need to determine the exceedance probabilities to support a Systems Acceptance Test based on collected data. Background A System Acceptance Test (SAT) requiring confirmatory data analysis (Box, Hunter, & Hunter, 2005) driven by apriori and politically deducted hypotheses is needed to assess the impact of a specific acquisition on two key system level performance parameters for a particular region: probability of detection (Pd) and probability of identification (Pid). The difficulty with this assessment is that JACYNA & ROSEN 537 within this region of interest, only a finite portion is covered by each sensor's area-of-regard (AOR). In addition, there are an infinite number of threat compositions and avenues of ingress and egress (i.e., routes) that are possible throughout the area. Only a small sampling of operationally valid (traversable by the threat) routes across the region is executed and these are used to characterize the performance measures across the entire area. See Figure 1 for an illustrative view of this concept. Figure 1. A high level illustration depicting the relationship among a project area and the sample routes, operational valid routes, and sensor areas-of-regards within it. The overwhelming size of the test area introduces an additional test constraint. This is addressed by approximating the route samples with segment-level performance observations by considering a segment to be a contiguous subset of a given route. Moreover, a trial in this system acceptance test is defined as being a test observation made on a single segment. The subset of segments chosen for the test fall within …

Developing Bayesian-based Confidence Bounds for Non-identically Distributed Observations using the Lyapunov Condition