Parameterizing Lognormal state space models using moment matching
Parameterizing Lognormal state space models using moment matching
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DOI：
10.1007/s10651-023-00570-x
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发表时间：
2023-07-15
影响因子：
3.8
通讯作者：
Johnson，Leah R.
中科院分区：
文献类型：
--
作者：
Smith，John W.;Thomas，R. Quinn;Johnson，Leah R.
在生态学中，基于系统的物理约束来限定进程是很常见的。一个常见的例子是积极约束，它适用于持续时间、人口规模和系统商品的总库存等现象。本文提出了一种基于矩匹配的对数正态状态空间模型的参数化方法。我们的方法实施了正性约束，允许任意的平均演化和方差结构，并且具有闭合形式的马尔可夫转移密度，这允许在拟合技术方面具有更大的灵活性。我们讨论了两个现有的对数正态状态空间模型，并研究了它们与本文提出的方法的不同之处。我们使用180个合成数据集比较了模型误指定情况下的预测性能，并评估了我们的方法与现有方法对参数精度的估计。我们发现，我们的模型在错误指定的情况下表现得很好，固定观测方差既有助于改善对过程方差的估计，又有助于提高预测性能。为了测试我们的方法在一个困难的问题上，我们比较了两个对数正态状态空间模型的预测性能，通过使用基于过程的生态系统模型来描述时间动态，预测151天范围内的叶面积指数。我们发现，我们的矩匹配模型比它的竞争对手表现得更好，更适合于中间预测视界。总体而言，我们的研究有助于告知从业者在使用复杂系统的模型预测样本外时纳入合理的动力学的重要性。
In ecology, it is common for processes to be bounded based on physical constraints of the system. One common example is the positivity constraint, which applies to phenomena such as duration times, population sizes, and total stock of a system’s commodity. In this paper, we propose a novel method for parameterizing Lognormal state space models using an approach based on moment matching. Our method enforces the positivity constraint, allows for arbitrary mean evolution and variance structure, and has a closed-form Markov transition density which allows for more flexibility in fitting techniques. We discuss two existing Lognormal state space models and examine how they differ from the method presented here. We use 180 synthetic datasets to compare the forecasting performance under model misspecification and assess the estimation of precision parameters between our method and existing methods. We find that our models perform well under misspecification, and that fixing the observation variance both helps to improve estimation of the process variance and improves forecast performance. To test our method on a difficult problem, we compare the predictive performance of two Lognormal state space models in predicting the Leaf Area Index over a 151 day horizon by using a process-based ecosystem model to describe the temporal dynamics. We find that our moment matching model performs better than its competitor, and is better suited for intermediate predictive horizons. Overall, our study helps to inform practitioners about the importance of incorporating sensible dynamics when using models of complex systems to predict out-of-sample.