Inference for reaction networks using the linear noise approximation
Inference for reaction networks using the linear noise approximation
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DOI：
10.1111/biom.12152
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发表时间：
2014-06-01
期刊：
影响因子：
1.9
通讯作者：
Sherlock, Chris
中科院分区：
文献类型：
--
作者：
Fearnhead, Paul;Giagos, Vasilieos;Sherlock, Chris
我们考虑在离散观测网络中的反应速率的推断，例如在系统生物学，种群生态学和流行病模型中发现的那些。大多数这样的网络既不够慢，也不够小，通过真正的状态依赖马尔可夫跳跃过程的推理是可行的。通常，通过常微分方程（ODE）或随机微分方程（ODE）近似动态来进行推断。前者忽略了真实模型中的随机性，可能导致不准确的推断。后者更准确，但更难实现，因为通常未知的转换密度的模型。线性噪声近似（LNA）是由确定性解的近似解的一阶泰勒展开式产生的，可以看作是常微分方程模型和非线性模型之间的折衷。这是一个随机模型，但LNA的离散时间转移概率可通过求解一系列常微分方程获得。我们描述了如何重新启动LNA可以有效地用于执行推理的一般类的反应网络，评估这种方法的准确性，并显示如何以及何时这种方法是统计或计算更有效的比ODE或ODE方法。我们应用LNA来分析来自新西兰北岛和南岛的谷歌流感趋势数据，并且能够获得比最近提出的另一种方法更准确的新流感病例的短期预测，尽管计算成本更高。
We consider inference for the reaction rates in discretely observed networks such as those found in models for systems biology, population ecology, and epidemics. Most such networks are neither slow enough nor small enough for inference via the true state-dependent Markov jump process to be feasible. Typically, inference is conducted by approximating the dynamics through an ordinary differential equation (ODE) or a stochastic differential equation (SDE). The former ignores the stochasticity in the true model and can lead to inaccurate inferences. The latter is more accurate but is harder to implement as the transition density of the SDE model is generally unknown. The linear noise approximation (LNA) arises from a first-order Taylor expansion of the approximating SDE about a deterministic solution and can be viewed as a compromise between the ODE and SDE models. It is a stochastic model, but discrete time transition probabilities for the LNA are available through the solution of a series of ordinary differential equations. We describe how a restarting LNA can be efficiently used to perform inference for a general class of reaction networks; evaluate the accuracy of such an approach; and show how and when this approach is either statistically or computationally more efficient than ODE or SDE methods. We apply the LNA to analyze Google Flu Trends data from the North and South Islands of New Zealand, and are able to obtain more accurate short-term forecasts of new flu cases than another recently proposed method, although at a greater computational cost.