捕获-再捕获模型贝叶斯分析中的后验检验
Examining posterior propriety in the Bayesian analysis of capture-recapture models
摘要：
将某些已知的数学结果应用于生态学，存在着潜在的危险。有些结果不适用于手头的问题。我们发现了这样一种趋势。基于数理统计中的几个定理，Link（2013）警告生态学家在某些条件下使用离散一致先验在分析中是不合适的，而是建议在分析过程中常规使用尺度先验。这一建议立即被生态学家广泛采纳。在这项研究中，我们考虑了两个基本的捕获-再捕获模型，广泛应用于生态学，$M_0$和$M_h$，并推导出后验适当的条件，通过检查的行为的右尾的后验分布的动物种群大小$N$在贝叶斯分析。我们证明了这两种可能性都比Link（2013）中考虑的可能性更有效。我们认为，没有特别的规范性的方法，应采取生态学家在选择先验的恐惧后不当。相反，我们建议的问题和手头的数据的可能性的有效建设，选择先验的现有知识的参数的利益，并鼓励检查后验适当的渐近参数，如本研究所示。
英文摘要：
There lies a latent danger in utilizing some known mathematical results in ecology. Some results do not apply to the problem at hand. We identify one such trend. Based on a couple of theorems in mathematical statistics, Link (2013) cautions ecologists about the inappropriateness of using the discrete uniform prior in their analysis under certain conditions and instead recommends the routine use of the scale prior during analysis. This recommendation is been absorbed immediately and widely among ecologists. In this study, we consider the two fundamental capture-recapture models used widely in ecology, $M_0$ and $M_h$, and derive conditions for posterior propriety by examining the behavior of the right tail of the posterior distributions of animal population size $N$ in a Bayesian analysis. We demonstrate that both these likelihoods are far more efficient than the ones considered in Link (2013). We argue that no particularly prescriptive approach should be adopted by ecologists in regard to choosing priors of the fear of posterior impropriety. Instead, we recommend the efficient construction of likelihoods for the problem and data on hand, choosing priors based existing knowledge of a parameter of interest and encourage examining posterior propriety by asymptotic arguments as demonstrated in this study.
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