Acoustic spatial capture-recapture (ASCR) surveys with an array of synchronized acoustic detectors can be an effective way of estimating animal density or call density. However, constructing the capture histories required for ASCR analysis is challenging, as recognizing which detections at different detectors are of which calls is not a trivial task. Because calls from different distances take different times to arrive at detectors, the order in which calls are detected is not necessarily the same as the order in which they are made, and without knowing which detections are of the same call, we do not know how many different calls are detected. We propose a Monte Carlo expectation-maximization (MCEM) estimation method to resolve this unknown call identity problem. To implement the MCEM method in this context, we sample the latent variables from a complete-data likelihood model in the expectation step and use a semi-complete-data likelihood or conditional likelihood in the maximization step. We use a parametric bootstrap to obtain confidence intervals. When we apply our method to a survey of moss frogs, it gives an estimate within 15% of the estimate obtained using data with call capture histories constructed by experts, and unlike this latter estimate, our confidence interval incorporates the uncertainty about call identities. Simulations show it to have a low bias (6%) and coverage probabilities close to the nominal 95% value.

翻译：使用同步声学探测器阵列进行声学空间捕获-再捕获（ASCR）调查是估计动物密度或叫声密度的有效方法。然而，构建ASCR分析所需的捕获历史具有挑战性，因为识别不同探测器检测到的声音对应哪些叫声并非易事。由于来自不同距离的叫声到达探测器所需时间不同，探测器检测到叫声的顺序不一定与叫声发出的顺序相同，且在不清楚哪些检测属于同一叫声的情况下，我们无法确定检测到了多少不同的叫声。我们提出了一种蒙特卡洛期望最大化（MCEM）估计方法来解决这一未知叫声身份问题。在此背景下实施MCEM方法时，我们在期望步中从完整数据似然模型中对潜变量进行抽样，并在最大化步中使用半完整数据似然或条件似然。我们采用参数自举法获得置信区间。将该方法应用于苔藓蛙调查时，其估计值与专家构建叫声捕获历史数据所得估计值的差异在15%以内，且与后者不同，我们的置信区间包含了叫声身份的不确定性。模拟实验表明该方法具有较低偏差（6%），且覆盖概率接近名义值95%。