很多生态系统都有混沌的或近乎混沌的动态。在这种情况下，难以验证相关数据是否符合具体模型，因为噪音使得与模型进行统计对比不可能进行。现在，Simon Wood设计了一个进行这种推断的统计模型，其所依据的是从原始数据提取对相位变化不敏感的汇总统计，并与从该模型模拟出的数据进行对比。研究人员通过对一个著名问题的应用演示了该方法，这个问题是：John Nicholson关于铜绿蝇(Lucilia cuprina)种群规模的经典生态实验中的周期的性质。（生物谷Bioon.com）
生物谷推荐原文出处：
Nature doi:10.1038/nature09319
Statistical inference for noisy nonlinear ecological dynamic systems
Simon N. Wood
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 trajectory1. 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 methods2, 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 experiments3, 4, 5.
