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首页> 外文期刊>Australian & New Zealand journal of statistics >ON VARIATIONAL BAYES ESTIMATION AND VARIATIONAL INFORMATION CRITERIA FOR LINEAR REGRESSION MODELS
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ON VARIATIONAL BAYES ESTIMATION AND VARIATIONAL INFORMATION CRITERIA FOR LINEAR REGRESSION MODELS

机译：线性回归模型的变数贝叶斯估计和变数信息准则

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摘要

Variational Bayes (VB) estimation is a fast alternative to Markov Chain Monte Carlo for performing approximate Baesian inference. This procedure can be an efficient and effective means of analyzing large datasets. However, VB estimation is often criticised, typically on empirical grounds, for being unable to produce valid statistical inferences. In this article we refute this criticism for one of the simplest models where Bayesian inference is not analytically tractable, that is, the Bayesian linear model (for a particular choice of priors). We prove that under mild regularity conditions, VB based estimators enjoy some desirable frequentist properties such as consistency and can be used to obtain asymptotically valid standard errors. In addition to these results we introduce two VB information criteria: the variational Akaike information criterion and the variational Bayesian information criterion. We show that variational Akaike information criterion is asymptotically equivalent to the frequentist Akaike information criterion and that the variational Bayesian information criterion is first order equivalent to the Bayesian information criterion in linear regression. These results motivate the potential use of the variational information criteria for more complex models. We support our theoretical results with numerical examples.
机译：变异贝叶斯（VB）估计是马尔可夫链蒙特卡洛算法的快速替代方案，用于执行近似贝叶斯推断。此过程可以是分析大型数据集的有效方法。但是，通常由于经验原因经常批评VB估计，因为它无法产生有效的统计推断。在本文中，我们对贝叶斯推论无法解析得出的最简单模型之一即贝叶斯线性模型（针对特定的先验选择）进行了反驳。我们证明，在适度的规律性条件下，基于VB的估计量具有一些理想的频繁性，例如一致性，可用于获得渐近有效的标准误差。除了这些结果之外，我们还介绍了两个VB信息标准：变型Akaike信息标准和变型贝叶斯信息标准。我们表明，线性回归分析中的变分Akaike信息准则渐近地等同于常客Akaike信息准则，而变分贝叶斯信息准则与贝叶斯信息准则一阶等效。这些结果激发了将变分信息标准用于更复杂模型的潜在用途。我们通过数值示例来支持我们的理论结果。

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