A standard way of formulating stochastic differential equation systems is to additively extend the drift of a deterministic system with a random diffusion part. But an increasing trend in applications, such as meteorology, is to perturb deterministic models in multiplicative and highly non-linear ways, that escape the standard framework. This work aims to present a Bayesian method that enables estimating the parameters of such systems. The approach is well suited for situations were the observation times are irregular with large gaps between, so that the use of usual prediction-based filtering methods is excluded. The key idea is to construct a likelihood that is based on feature vectors that characterize the variability of the system. We illustrate the capability of the method in different scenarios that are both chaotic and stochastic using the classical Lorenz system as the demonstration example.

中文翻译：

---

随机混沌系统的参数估计

制定随机微分方程系统的标准方法是累加扩展具有随机扩散部分的确定性系统的漂移。但是，在诸如气象学等应用程序中，越来越多的趋势是以乘法和高度非线性的方式干扰确定性模型，这些方法逃避了标准框架。这项工作旨在提出一种贝叶斯方法，该方法能够估算此类系统的参数。该方法非常适用于观测时间不规则且间隔较大的情况，因此排除了使用基于预测的常规滤波方法。关键思想是基于特征向量构建一种可能性，该特征向量表征系统的可变性。