论文标题
GLMM的MCMC
MCMC for GLMMs
论文作者
论文摘要
广义线性混合模型（GLMM）通常用于分析相关的非高斯数据。 GLMM中的似然函数仅作为高维积分可用，因此GLMM无法进行封闭形式的推断和预测。由于封闭形式不可用，因此贝叶斯GLMM的相关后密度也很棘手。通常，马尔可夫链蒙特卡洛（MCMC）算法用于GLMM中的有条件模拟并探索这些后密度。在本文中，我们介绍了用于拟合GLMM的最先进的MCMC算法。这些MCMC算法包括有效的数据增强策略，以及基于扩散和基于汉密尔顿动力学的方法。此处介绍的Langevin和Hamiltonian Monte Carlo方法适用于任何GLMM，并使用三个最受欢迎的GLMM进行了说明，即用于二项式数据的逻辑和概率GLMM，以及用于计数数据的Poisson-Log GLMM。我们还提出了用于概率和逻辑GLMM的有效数据增强算法。这些算法中的一些使用数值示例进行了比较。
Generalized linear mixed models (GLMMs) are often used for analyzing correlated non-Gaussian data. The likelihood function in a GLMM is available only as a high dimensional integral, and thus closed-form inference and prediction are not possible for GLMMs. Since the likelihood is not available in a closed-form, the associated posterior densities in Bayesian GLMMs are also intractable. Generally, Markov chain Monte Carlo (MCMC) algorithms are used for conditional simulation in GLMMs and exploring these posterior densities. In this article, we present different state of the art MCMC algorithms for fitting GLMMs. These MCMC algorithms include efficient data augmentation strategies, as well as diffusions based and Hamiltonian dynamics based methods. The Langevin and Hamiltonian Monte Carlo methods presented here are applicable to any GLMMs, and are illustrated using three most popular GLMMs, namely, the logistic and probit GLMMs for binomial data and the Poisson-log GLMM for count data. We also present efficient data augmentation algorithms for probit and logistic GLMMs. Some of these algorithms are compared using a numerical example.
