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Statistical inference for noisy nonlinear ecological dynamic systems

机译：噪声非线性生态动力学系统的统计推断

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摘要

Chaotic ecological dynamic systems defy conventional statistical analysis. Systems with near-chaotic dynamics are little better. Such systems are almost invariably driven by endogenous dynamic processes plus demographic and environmental process noise, and are only observable with error. Their sensitivity to history means that minute changes in the driving noise realization, or the system parameters, will cause drastic changes in the system trajectory. This sensitivity is inherited and amplified by the joint probability density of the observable data and the process noise, rendering it useless as the basis for obtaining measures of statistical fit. Because the joint density is the basis for the fit measures used by all conventional statistical methods, this is a major theoretical shortcoming. The inability to make well-founded statistical inferences about biological dynamic models in the chaotic and near-chaotic regimes, other than on an ad hoc basis, leaves dynamic theory without the methods of quantitative validation that are essential tools in the rest of biological science. Here I show that this impasse can be resolved in a simple and general manner, using a method that requires only the ability to simulate the observed data on a system from the dynamic model about which inferences are required. The raw data series are reduced to phase-insensitive summary statistics, quantifying local dynamic structure and the distribution of observations. Simulation is used to obtain the mean and the covariance matrix of the statistics, given model parameters, allowing the construction of a 'synthetic likelihood' that assesses model fit. This likelihood can be explored using a straightforward Markov chain Monte Carlo sampler, but one further post-processing step returns pure likelihood-based inference. I apply the method to establish the dynamic nature of the fluctuations in Nicholson's classic blowfly experiments.
机译：混沌生态动力学系统无视常规的统计分析。具有近乎混沌动力学的系统要好一些。此类系统几乎总是由内源性动态过程以及人口统计和环境过程噪声驱动，并且只能观察到错误。它们对历史的敏感性意味着行驶噪声实现或系统参数的微小变化将导致系统轨迹的急剧变化。这种敏感性是通过可观察数据和过程噪声的联合概率密度来继承和放大的，从而使其无法用作获取统计拟合度量的基础。因为关节密度是所有常规统计方法所采用的拟合度量的基础，所以这是一个主要的理论缺陷。除了在临时基础上，无法在混沌和接近混沌状态下就生物学动力学模型做出有根据的统计推论，使得动力学理论没有其他生物学科学必不可少的定量验证方法。在这里，我表明，这种僵局可以使用一种方法来简单，通用地解决，该方法仅需要能够从需要进行推理的动态模型中模拟系统上观察到的数据的能力。原始数据系列被简化为对相位不敏感的汇总统计信息，从而量化了局部动态结构和观测值的分布。在给定模型参数的情况下，使用仿真来获得统计数据的均值和协方差矩阵，从而可以构建评估模型拟合度的“综合可能性”。可以使用直接的马尔可夫链蒙特卡洛采样器来探索这种可能性，但是进一步的后处理步骤将返回基于纯似然性的推断。我应用该方法建立了Nicholson经典吹蝇实验中波动的动态性质。

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  • 来源
    《Nature》 |2010年第7310期|P.1102-1104iiiv|共5页
  • 作者

    Simon N. Wood;

  • 作者单位

    Mathematical Sciences, University of Bath, Bath BA2 7AY, UK;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);美国《生物学医学文摘》(MEDLINE);美国《化学文摘》(CA);
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  • 正文语种 eng
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