论文标题
贝叶斯P型模型中对拉普拉斯近似的惩罚参数选择和不对称校正
Penalty parameter selection and asymmetry corrections to Laplace approximations in Bayesian P-splines models
论文作者
论文摘要
Laplacian-P-Splines（LPS）将P-Splines更加顺畅，Laplace近似在贝叶斯范式下的快速和灵活推断的统一框架中均匀。高斯马尔可夫田野先验对被惩罚的潜在变量和伯恩斯坦 - 冯·米斯定理（Bernstein-von Mises therorem）施加了，通常确保拉普拉斯近似与这些变量后验分布的剃须刀近似精度。对于某些未确定的参数，这种准确性可能会严重损害，尤其是当先验和可能性稀少的信息综合时。我们通过将潜在空间分为两个子集，提出了LPS方法的精致版本。第一组涉及潜在变量，从非高斯的角度接近联合后验分布，其近似方案尤其是为捕获不对称模式而定制的近似方案，而互补潜伏组中参数的后验分布经历了带有laplace近似值的传统处理。因此，潜在空间的二分法为单独处理模型参数提供了必要的结构，与使用拉普拉斯均匀处理的设置相比，可以提高估计精度。此外，提议的丰富版本的LPS仍然完全不含采样，因此它以远离任何现有Markov Chain Monte Carlo方法的计算速度运行。该方法在添加性比例赔率模型上使用序数调查数据进行了说明。
Laplacian-P-splines (LPS) associate the P-splines smoother and the Laplace approximation in a unifying framework for fast and flexible inference under the Bayesian paradigm. Gaussian Markov field priors imposed on penalized latent variables and the Bernstein-von Mises theorem typically ensure a razor-sharp accuracy of the Laplace approximation to the posterior distribution of these variables. This accuracy can be seriously compromised for some unpenalized parameters, especially when the information synthesized by the prior and the likelihood is sparse. We propose a refined version of the LPS methodology by splitting the latent space in two subsets. The first set involves latent variables for which the joint posterior distribution is approached from a non-Gaussian perspective with an approximation scheme that is particularly well tailored to capture asymmetric patterns, while the posterior distribution for parameters in the complementary latent set undergoes a traditional treatment with Laplace approximations. As such, the dichotomization of the latent space provides the necessary structure for a separate treatment of model parameters, yielding improved estimation accuracy as compared to a setting where posterior quantities are uniformly handled with Laplace. In addition, the proposed enriched version of LPS remains entirely sampling-free, so that it operates at a computing speed that is far from reach to any existing Markov chain Monte Carlo approach. The methodology is illustrated on the additive proportional odds model with an application on ordinal survey data.
