Data augmentation improves the convergence of iterative algorithms, such as the EM algorithm and Gibbs sampler by introducing carefully designed latent variables. In this article, we first propose a data augmentation scheme for the first-order autoregression plus noise model, where optimal values of working parameters introduced for recentering and rescaling of the latent states, can be derived analytically by minimizing the fraction of missing information in the EM algorithm. The proposed data augmentation scheme is then utilized to design efficient Markov chain Monte Carlo (MCMC) algorithms for Bayesian inference of some non-Gaussian and nonlinear state space models, via a mixture of normals approximation coupled with a block-specific reparametrization strategy. Applications on simulated and benchmark real datasets indicate that the proposed MCMC sampler can yield improvements in simulation efficiency compared with centering, noncentering and even the ancillarity-sufficiency interweaving strategy.
翻译:数据增强通过引入精心设计的潜伏变量,提高了迭代算法(如EM算法和Gibbs取样器)的趋同程度。在本篇文章中,我们首先为第一级自动反向和噪音模型提出了一个数据增强计划,通过这一计划,可以通过将EM算法中缺失的信息的一小部分降到最低程度,从而分析地得出为潜伏状态的更新和调整而引入的工作参数的最佳值。 拟议的数据增强计划随后被用来设计高效的Markov连锁 Monte Carlo(MCMC)算法,用于一些非Gausian和非线性国家空间模型的巴伊西语推理推理,其方法是将正常的近似结合成一个具体区块的再平衡战略。 在模拟和基准实际数据集的应用中,拟议的MC取样器可以提高模拟效率,而与中心、非中心、不集中甚至超常-充足交织战略相比。