带复误差过程和动态Markov基的隐多项式模型的推广
Extending the Latent Multinomial Model with Complex Error Processes and Dynamic Markov Bases
摘要：
Link等人（2010年）的潜在多项模型（LMM）模型提供了一个通用框架，用于对识别中存在潜在错误的标记-再捕获数据进行建模。这种方法的关键是一个马尔可夫链蒙特卡罗（MCMC）计划抽样可能的配置的计数真实的捕获历史，可能产生的观测数据。该MCMC算法使用来自真实计数和观测计数之间的线性映射的核的基础的向量，以在真实数据的可能配置之间移动。Schofield和Bonner（2015）表明，严格的基础对于一些误差模型是足够的，包括Link等人提出的模型。我们用这种方法解决了两个进一步的挑战：1）具有更复杂错误机制的模型不容易适合LMM，2）即使是中等规模的研究，马尔可夫基础也很难或不可能计算。我们解决这些问题，通过扩展LMM分别建模的捕获/人口统计过程和错误的过程，并通过开发一个新的MCMC抽样方案，使用动态马尔可夫基础。我们的工作是出于对美国肯塔基州皇后蛇（Regina septemvittata）的研究，我们使用模拟来比较PIT标签的使用，具有完美的识别，以及在估计存活率时容易出错的品牌。
英文摘要：
The latent multinomial model (LMM) model of Link et al. (2010) provided a general framework for modelling mark-recapture data with potential errors in identification. Key to this approach was a Markov chain Monte Carlo (MCMC) scheme for sampling possible configurations of the counts true capture histories that could have generated the observed data. This MCMC algorithm used vectors from a basis for the kernel of the linear map between the true and observed counts to move between the possible configurations of the true data. Schofield and Bonner (2015) showed that a strict basis was sufficient for some models of the errors, including the model presented by Link et al. (2010), but a larger set called a Markov basis may be required for more complex models. We address two further challenges with this approach: 1) that models with more complex error mechanisms do not fit easily within the LMM and 2) that the Markov basis can be difficult or impossible to compute for even moderate sized studies. We address these issues by extending the LMM to separately model the capture/demographic process and the error process and by developing a new MCMC sampling scheme using dynamic Markov bases. Our work is motivated by a study of Queen snakes (Regina septemvittata) in Kentucky, USA, and we use simulation to compare the use of PIT tags, with perfect identification, and brands, which are prone to error, when estimating survival rates.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
