Quasi-Bayesian Inference for Latent Variable Models with External Information: Application to generalized linear mixed models for biased data
Quasi-Bayesian Inference for Latent Variable Models with External Information: Application to generalized linear mixed models for biased data
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发表时间：
2017-04
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通讯作者：
T. Hoshino;R. Igari
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作者：
T. Hoshino;R. Igari
有大量的文献提出了非贝叶斯方法，用于结合辅助信息（如人口水平的边缘矩）进行推断。然而，它是不可行的，直接将这些方法应用于潜变量模型，因为数据增强的方法，其中潜变量被视为附带参数，然后生成，没有开发。在本文中，我们提出了一个马尔可夫链蒙特卡罗（MCMC）算法与数据增强的潜变量模型的情况下，我们有一个采样数据集和额外的信息，如人口水平的时刻。所得到的带有辅助信息的拟贝叶斯推断实现起来非常简单，本文给出了MCMC输出的拟贝叶斯后验均值估计的相合性和渐近方差。该方法是特别有用的，当数据集是有偏的，但我们有一个无偏的大样本的一些变量或人口的边缘时刻，这是很难正确地指定样本选择模型。为了说明的目的，我们应用所提出的估计方法，广义线性混合模型的有偏数据在模拟研究和真实的数据分析。所提出的方法可以用来在非/半参数潜变量模型中进行推断，通过将现有的半参数贝叶斯算法，如在MCMC迭代的块吉布斯采样。
There is a vast literature proposing non-Bayesian methods for making inferences incorporating auxiliary information such as population-level marginal moments. However, it is not feasible to apply these methods directly to latent variable models because the data augmentation approach, in which latent variables are treated as incidental parameters and then generated, is not developed. In this paper, we propose a Markov Chain Monte Carlo (MCMC) algorithm with data augmentation for latent variable models for cases in which we have both a sampled dataset and additional information such as population level moments. The resulting quasi-Bayesian inference with auxiliary information is very straightforwaed to implement, and consistency and asymptotic variance of the quasi- Bayesian posterior mean estimators from the MCMC outputs are shown in this paper. The proposed method is especially useful when the dataset is biased but we have an unbiased large sample for some variables or population marginal moments in which it is difficult to correctly specify the sample selection model. For illustrative purposes, we apply the proposed estimation method to generalized linear mixed models for biased data both in simulation studies and in real data analysis. The proposed method can be used to make inferences in non/semi-parametric latent variable models by incorporating the existing semi-parametric Bayesian algorithms such as the Blocked Gibbs sampler in the MCMC iteration.