Bayesian analysis of the covariance matrix of a multivariate normal distribution with a new class of priors

IF 4.3 3区 材料科学 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC
J. Berger, Dongchu Sun, Chengyuan Song
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引用次数: 7

Abstract

Bayesian analysis for the covariance matrix of a multivariate normal distribution has received a lot of attention in the last two decades. In this paper, we propose a new class of priors for the covariance matrix, including both inverse Wishart and reference priors as special cases. The main motivation for the new class is to have available priors – both subjective and objective – that do not “force eigenvalues apart,” which is a criticism of inverse Wishart and Jeffreys priors. Extensive comparison of these ‘shrinkage priors’ with inverse Wishart and Jeffreys priors is undertaken, with the new priors seeming to have considerably better performance. A number of curious facts about the new priors are also observed, such as that the posterior distribution will be proper with just three vector observations from the multivariate normal distribution – regardless of the dimension of the covariance matrix – and that useful inference about features of the covariance matrix can be possible. Finally, a new MCMC algorithm is developed for this class of priors and is shown to be computationally effective for matrices of up to 100 dimensions.
具有一类新先验的多元正态分布协方差矩阵的贝叶斯分析
多元正态分布协方差矩阵的贝叶斯分析在过去二十年中受到了很多关注。在本文中,我们为协方差矩阵提出了一类新的先验,包括作为特例的逆Wishart和参考先验。新类别的主要动机是拥有可用的先验——包括主观和客观先验——它们不会“迫使特征值分离”,这是对逆Wishart和Jeffreys先验的批评。对这些“收缩先验”与逆Wishart和Jeffreys先验进行了广泛的比较,新的先验似乎具有更好的性能。还观察到了一些关于新先验的奇怪事实,例如,无论协方差矩阵的维度如何,多元正态分布中只有三个向量观测值的后验分布是正确的,并且可以对协方差矩阵的特征进行有用的推断。最后,为这类先验开发了一种新的MCMC算法,该算法对高达100维的矩阵在计算上是有效的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
7.20
自引率
4.30%
发文量
567
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