State space models play an important role in macroeconometric analysis and the Bayesian approach has been shown to have many advantages. This paper outlines recent developments in state space modelling applied to macroeconomics using Bayesian methods. We outline the directions of recent research, specifically the problems being addressed and the solutions proposed. After presenting a general form for the linear Gaussian model, we discuss the interpretations and virtues of alternative estimation routines and their outputs. This discussion includes the Kalman filter and smoother, and precision-based algorithms. As the advantages of using large models have become better understood, a focus has developed on dimension reduction and computational advances to cope with high-dimensional parameter spaces. We give an overview of a number of recent advances in these directions. Many models suggested by economic theory are either non-linear or non-Gaussian, or both. We discuss work on the particle filtering approach to such models as well as other techniques that use various approximations – to either the time state and measurement equations or to the full posterior for the states – to obtain draws.

中文翻译：

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宏观经济学中的贝叶斯状态空间模型

状态空间模型在宏观计量分析中起着重要作用，贝叶斯方法已被证明具有许多优势。本文概述了使用贝叶斯方法应用于宏观经济学的状态空间建模的最新进展。我们概述了近期研究的方向，特别是正在解决的问题和提出的解决方案。在介绍了线性高斯模型的一般形式之后，我们讨论了替代估计例程及其输出的解释和优点。此讨论包括卡尔曼滤波器和平滑器以及基于精度的算法。随着使用大型模型的优势得到更好的理解，人们开始关注降维和计算进步，以应对高维参数空间。我们概述了这些方向的一些最新进展。经济理论提出的许多模型要么是非线性的，要么是非高斯模型，或者两者兼而有之。我们讨论了此类模型的粒子滤波方法以及使用各种近似值的其他技术的工作——无论是时间状态和测量方程或状态的完整后验 - 获得平局。