论文标题
动态回归模型的动态稀疏性
Dynamic sparsity on dynamic regression models
论文作者
论文摘要
在目前的工作中，我们考虑了贝叶斯框架内高斯动态线性回归的可变选择和收缩。特别是，我们提出了一种新的方法，该方法允许在动态模型的尖峰和刻录式先验的扩展基础上扩展时间变化的稀疏度。这是通过为随时间变化系数的方差分配适当的马尔可夫切换先验来完成的，从而扩展了Ishwaran和Rao（2005）的先前工作。此外，我们研究了过程差异的不同先验的不同先验，以及其他混合物的先验分布，例如尖峰和平板的伽玛先验，这会导致正常伽马西亚先验的混合物（Griffin Ad Brown，2010年）。从这个意义上讲，我们的先验可以视为一个动态变量选择，在每个时间点都会诱导平滑度（通过平板）或向零（通过尖峰）收缩。用于后验计算的MCMC方法使用Markov潜在变量，可以在每个时间点假设二进制方案来生成系数的方差。这样，我们的模型是动态混合模型，因此，我们可以使用Gerlach等人（2000）的算法来生成潜在过程，而无需在状态下进行调节。最后，通过模拟示例和真实的数据应用程序来说明我们的方法。
In the present work, we consider variable selection and shrinkage for the Gaussian dynamic linear regression within a Bayesian framework. In particular, we propose a novel method that allows for time-varying sparsity, based on an extension of spike-and-slab priors for dynamic models. This is done by assigning appropriate Markov switching priors for the time-varying coefficients' variances, extending the previous work of Ishwaran and Rao (2005). Furthermore, we investigate different priors, including the common Inverted gamma prior for the process variances, and other mixture prior distributions such as Gamma priors for both the spike and the slab, which leads to a mixture of Normal-Gammas priors (Griffin ad Brown, 2010) for the coefficients. In this sense, our prior can be view as a dynamic variable selection prior which induces either smoothness (through the slab) or shrinkage towards zero (through the spike) at each time point. The MCMC method used for posterior computation uses Markov latent variables that can assume binary regimes at each time point to generate the coefficients' variances. In that way, our model is a dynamic mixture model, thus, we could use the algorithm of Gerlach et al (2000) to generate the latent processes without conditioning on the states. Finally, our approach is exemplified through simulated examples and a real data application.
