This paper considers the problem of computing Bayesian estimates of both states and model parameters for nonlinear state-space models. Generally, this problem does not have a tractable solution and approximations must be utilised. In this work, a variational approach is used to provide an assumed density which approximates the desired, intractable, distribution. The approach is deterministic and results in an optimisation problem of a standard form. Due to the parametrisation of the assumed density selected first- and second-order derivatives are readily available which allows for efficient solutions. The proposed method is compared against state-of-the-art Hamiltonian Monte Carlo in two numerical examples.

翻译：本文件审议了计算巴伊西亚州和非线性国家空间模型的估算值和模型参数的问题。 一般而言,这一问题没有可伸缩的解决方案,必须使用近似值。在这项工作中,采用了一种变式方法来提供一种假定密度,接近理想的、棘手的、分布的密度。这种方法具有确定性,导致标准格式的优化问题。由于假定的第一和第二级衍生物密度的平衡化,很容易找到有效的解决方案。在两个数字例子中,将拟议方法与最先进的汉密尔顿·蒙特卡洛比较。