Prior choice and data requirements of Bayesian multivariate mixed effects models fit to tag-recovery data: The need for power analyses

1. Recent empirical studies have quantified correlation between survival
and recovery by estimating these parameters as correlated random effects
with hierarchical Bayesian multivariate models fit to tag-recovery data.
In these applications, increasingly negative correlation between survival
and recovery has been interpreted as evidence for increasingly additive
harvest mortality. The power of these hierarchal models to detect non-zero
correlations has rarely been evaluated and these few studies have not
focused on tag-recovery data, which is a common data type. 2. We assessed
the power of multivariate hierarchical models to detect negative
correlation between annual survival and recovery. Using three priors for
multivariate normal distributions, we fit hierarchical effects models to a
mallard (Anas platyrhychos) tag-recovery dataset and to simulated data
with sample sizes corresponding to different levels of monitoring
intensity. We also demonstrate more robust summary statistics for
tag-recovery datasets than total individuals tagged. 3. Different priors
lead to substantially different estimates of correlation from the mallard
data. Our power analysis of simulated data indicated most prior
distribution and sample size combinations could not estimate strongly
negative correlation with useful precision or accuracy. Many correlation
estimates spanned the available parameter space (–1,1) and underestimated
the magnitude of negative correlation. Only one prior combined with our
most intensive monitoring scenario provided reliable results.
Underestimating the magnitude of correlation coincided with overestimating
the variability of annual survival, but not annual recovery. 4. The
inadequacy of prior distributions and sample size combinations previously
assumed adequate for obtaining robust inference from tag-recovery data
represents a concern in the application of Bayesian hierarchical models to
tag-recovery data. Our analysis approach provides a means for examining
prior influence and sample size on hierarchical models fit to
capture-recapture data while emphasizing transferability of results
between empirical and simulation studies.

1. 近期的实证研究通过将生存与恢复参数作为相关随机效应（random effects），结合适配标记回收数据（tag-recovery data）的分层贝叶斯多变量模型（hierarchical Bayesian multivariate models）进行估计，量化了二者间的相关性。在这类应用中，生存与恢复间的负相关性不断增强，常被解读为累加性捕捞死亡率上升的证据。这类分层模型检测非零相关性的检验效能（power）罕有评估，且现有少量相关研究均未聚焦于标记回收数据这一常用数据类型。
2. 本研究旨在评估多变量分层模型检测年度生存与恢复间负相关性的检验效能。我们采用三种多变量正态分布（multivariate normal distributions）先验（prior），将分层效应模型适配于绿头鸭（mallard, *Anas platyrhychos*）标记回收数据集，以及对应不同监测强度水平的模拟数据集。此外，本研究还提出了相较于标记总个体数更具稳健性的标记回收数据集汇总统计量。
3. 针对绿头鸭数据集，不同先验会导致相关性估计结果出现显著差异。我们对模拟数据开展的检验效能分析显示，多数先验分布与样本量的组合无法以具备实用价值的精度与准确性估算强负相关性。大量相关性估计值覆盖了参数空间(-1,1)的全部范围，且低估了负相关性的强度。仅有一种先验与本研究最高强度监测场景相结合时，可得到可靠的估计结果。相关性强度的低估，与年度生存变异性的高估相伴而生，但与年度恢复变异性的高估无关。
4. 此前被认为可从标记回收数据中获取稳健推断的先验分布与样本量组合存在不足，这一问题给贝叶斯分层模型在标记回收数据中的应用带来了隐患。本研究的分析方法为探究先验影响与样本量对适配捕获再捕获数据（capture-recapture data）的分层模型的作用提供了途径，同时强调了实证研究与模拟研究间结果的可迁移性。