Population time series: Process variability, observation errors, missing values, lags, and hidden states
Population time series: Process variability, observation errors, missing values, lags, and hidden states
复制标题
DOI：
10.1890/03-0520
复制
发表时间：
2004-11-01
期刊：
影响因子：
4.8
通讯作者：
Bjornstad, ON
中科院分区：
文献类型：
--
作者：
Clark, JS;Bjornstad, ON
人口样本数据很复杂；推论和预测不仅需要确定预期未来丰度的非线性相互作用，还需要数据和可变（通常是未观察到的）环境因素中固有的随机性。此外，人口普查可能会偶尔发生，并且观察误差随样本方法和精力而变化。状态变量（通常是密度或丰度）可以被隐藏，并且只能通过高度间接的观察方案（例如公共卫生记录，狩猎报告或化石/考古调查）而闻名。我们扩展了时间序列分析的基本状态空间模型，以适应影响人群数据的这些主要变异源。使用示例，我们展示了如何在贝叶斯状态空间模型的灵活框架内考虑不同类型的过程误差和观察错误，不相等的样本间隔和缺失值。我们提供基于吉布斯采样的算法，可用于获得人口状态和模型参数的后验估计。对于可以线性化的模型，结果可用于直接采样后验，包括那些值缺失的值和不等的采样间隔。对于非线性模型，我们利用Gibbs采样框架内的大都市杂货店。示例来自长期人口普查和人口数据。我们说明了使用时间序列的20世纪中期的易感性重新授予（TSIR）模型的时间序列的分离状态变量的扩展，该模型已知，在伦敦，假定出生率已知，但受感染者和不完美的个体出现了。报告。
Population sample data are complex; inference and prediction require proper accommodation of not only the nonlinear interactions that determine the expected future abundance, but also the stochasticity inherent in data and variable (often unobserved) environmental factors. Moreover, censuses may occur sporadically, and observation errors change with sample methods and effort. The state variable (usually density or abundance) may be hidden from view and known only through highly indirect observational schemes (such as public health records, hunting reports, or fossil/archeological surveys). We extend the basic state-space model for time-series analysis to accommodate these dominant sources of variability that influence population data. Using examples, we show how different types of process error and observation error, unequal sample intervals, and missing values can be accounted for within the flexible framework of Bayesian state-space models. We provide algorithms based on Gibbs sampling that can be used to obtain posterior estimates of population states and of model parameters. For models that can be linearized, results can be used for direct sampling of the posterior, including those with missing values and unequal sample intervals. For nonlinear models, we make use of Metropolis-Hastings within the Gibbs sampling framework. Examples derive from long-term census and population data. We illustrate the extension to discrete state variables with multiple stages using a Time-series Susceptible-Infected-Recovered (TSIR) model for mid 20th-century measles infection in London, where birth rates are assumed known, but susceptibles and infected individuals arise from imperfect reporting.