{"title":"具有时间检测数据的 N 混合物模型的精确似然值","authors":"Linda M. Haines, Res Altwegg, D. L. Borchers","doi":"10.1111/anzs.12401","DOIUrl":null,"url":null,"abstract":"This paper is concerned with the formulation of <math altimg=\"urn:x-wiley:anzs:media:anzs12401:anzs12401-math-0001\" display=\"inline\" location=\"graphic/anzs12401-math-0001.png\" overflow=\"scroll\">\n<semantics>\n<mrow>\n<mi>N</mi>\n</mrow>\n$$ N $$</annotation>\n</semantics></math>-mixture models for estimating the abundance and probability of detection of a species from binary response, count and time-to-detection data. A modelling framework, which encompasses time-to-first-detection within the context of detection/non-detection and time-to-each-detection and time-to-first-detection within the context of count data, is introduced. Two observation processes which depend on whether or not double counting is assumed to occur are also considered. The main focus of the paper is on the derivation of explicit forms for the likelihoods associated with each of the proposed models. Closed-form expressions for the likelihoods associated with time-to-detection data are new and are developed from the theory of order statistics. A key finding of the study is that, based on the assumption of no double counting, the likelihoods associated with times-to-detection together with count data are the product of the likelihood for the counts alone and a term which depends on the detection probability parameter. This result demonstrates that, in this case, recording times-to-detection could well improve precision in estimation over recording counts alone. In contrast, for the double counting protocol with exponential arrival times, no information was found to be gained by recording times-to-detection in addition to the count data. An <span style=\"font-family:sans-serif\">R</span> package and an accompanying vignette are also introduced in order to complement the algebraic results and to demonstrate the use of the models in practice.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Exact likelihoods for N-mixture models with time-to-detection data\",\"authors\":\"Linda M. Haines, Res Altwegg, D. L. Borchers\",\"doi\":\"10.1111/anzs.12401\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper is concerned with the formulation of <math altimg=\\\"urn:x-wiley:anzs:media:anzs12401:anzs12401-math-0001\\\" display=\\\"inline\\\" location=\\\"graphic/anzs12401-math-0001.png\\\" overflow=\\\"scroll\\\">\\n<semantics>\\n<mrow>\\n<mi>N</mi>\\n</mrow>\\n$$ N $$</annotation>\\n</semantics></math>-mixture models for estimating the abundance and probability of detection of a species from binary response, count and time-to-detection data. A modelling framework, which encompasses time-to-first-detection within the context of detection/non-detection and time-to-each-detection and time-to-first-detection within the context of count data, is introduced. Two observation processes which depend on whether or not double counting is assumed to occur are also considered. The main focus of the paper is on the derivation of explicit forms for the likelihoods associated with each of the proposed models. Closed-form expressions for the likelihoods associated with time-to-detection data are new and are developed from the theory of order statistics. A key finding of the study is that, based on the assumption of no double counting, the likelihoods associated with times-to-detection together with count data are the product of the likelihood for the counts alone and a term which depends on the detection probability parameter. This result demonstrates that, in this case, recording times-to-detection could well improve precision in estimation over recording counts alone. In contrast, for the double counting protocol with exponential arrival times, no information was found to be gained by recording times-to-detection in addition to the count data. 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引用次数: 0
摘要
本文涉及 N$$ N$ 混合模型的建立,用于从二元响应、计数和检测时间数据中估计物种的丰度和检测概率。本文介绍了一个建模框架,其中包括检测/未检测背景下的首次检测时间,以及计数数据背景下的每次检测时间和首次检测时间。此外,还考虑了取决于是否假设发生重复计数的两个观测过程。本文的主要重点是推导与每个建议模型相关的似然的明确形式。与时间检测数据相关的似然的闭式表达是新的,是从阶次统计理论中发展出来的。研究的一个重要发现是,基于无重复计数的假设,与检测时间和计数数据相关的似然值是单独计数似然值与一个取决于检测概率参数的项的乘积。这一结果表明,在这种情况下,记录检测时间比单独记录计数更能提高估算精度。与此相反,对于指数到达时间的双重计数协议,除了计数数据外,记录检测时间也无法获得任何信息。为了补充代数结果并演示模型的实际应用,我们还介绍了一个 R 软件包和随附的小故事。
Exact likelihoods for N-mixture models with time-to-detection data
This paper is concerned with the formulation of -mixture models for estimating the abundance and probability of detection of a species from binary response, count and time-to-detection data. A modelling framework, which encompasses time-to-first-detection within the context of detection/non-detection and time-to-each-detection and time-to-first-detection within the context of count data, is introduced. Two observation processes which depend on whether or not double counting is assumed to occur are also considered. The main focus of the paper is on the derivation of explicit forms for the likelihoods associated with each of the proposed models. Closed-form expressions for the likelihoods associated with time-to-detection data are new and are developed from the theory of order statistics. A key finding of the study is that, based on the assumption of no double counting, the likelihoods associated with times-to-detection together with count data are the product of the likelihood for the counts alone and a term which depends on the detection probability parameter. This result demonstrates that, in this case, recording times-to-detection could well improve precision in estimation over recording counts alone. In contrast, for the double counting protocol with exponential arrival times, no information was found to be gained by recording times-to-detection in addition to the count data. An R package and an accompanying vignette are also introduced in order to complement the algebraic results and to demonstrate the use of the models in practice.