We consider the problem of evaluating dynamic consistency in discrete time
probabilistic filters that approximate stochastic system state densities with
Gaussian mixtures. Dynamic consistency means that the estimated probability
distributions correctly describe the actual uncertainties. As such, the problem
of consistency testing naturally arises in applications with regards to
estimator tuning and validation. However, due to the general complexity of the
density functions involved, straightforward approaches for consistency testing
of mixture-based estimators have remained challenging to define and implement.
This paper derives a new exact result for Gaussian mixture consistency testing
within the framework of normalized deviation squared (NDS) statistics. It is
shown that NDS test statistics for generic multivariate Gaussian mixture models
exactly follow mixtures of generalized chi-square distributions, for which
efficient computational tools are available. The accuracy and utility of the
resulting consistency tests are numerically demonstrated on static and dynamic
mixture estimation examples.

我们考虑在逼近具有混合高斯态的随机系统状态密度的离散时间概率滤波器的动态一致性评估问题。本文推导了在标准化偏差平方（NDS）统计框架内，用于高斯混合一致性测试的新的精确结果，显示出用于一般多变量高斯混合模型的 NDS 检验统计量确切遵循广义卡方分布的混合分布，进而演示了其在静态和动态混合估计示例中的准确性和实用性。

利用标准化偏差平方统计量对高斯混合滤波器进行精确一致性测试

Exact Consistency Tests for Gaussian Mixture Filters using Normalized  Deviation Squared Statistics

In this chapter, we will first present the most standard computational
challenges met in Bayesian Statistics, focussing primarily on mixture
estimation and on model choice issues, and then relate these problems with
computational solutions. Of course, this chapter is only a terse introduction
to the problems and solutions related to Bayesian computations. For more
complete references, see Robert and Casella (2004, 2009), or Marin and Robert
(2007), among others. We also restrain from providing an introduction to
Bayesian Statistics per se and for comprehensive coverage, address the reader
to Robert (2007), (again) among others.

介绍了贝叶斯统计中的混合估计和模型选择问题，以及与之相关的计算解决方案，参考文献主要为 Robert 和 Casella (2004, 2009) 和 Marin 和 Robert (2007) 等。