论文标题
结合化合物对称高斯模型的贝叶斯分析
Conjugate Bayesian analysis of compound-symmetric Gaussian models
论文作者
论文摘要
我们讨论了具有复合对称方差互动矩阵的已知均值高斯模型的贝叶斯推断。由于此类矩阵的空间是正定矩阵的线性子空间，因此我们利用Pisano（2022）的方法分解了通常的Wishart共轭物，并得出了封闭形式的三参数，三变形的，双变量的比变量，对化合物中对称半分子的基质进行了先验分布。发现异对管条目在对角线上具有非中心的Kummer-beta分布，该分布在对角线上具有γ分布，该伽马分布概括为高斯的超几何函数。这种考虑因素对高斯环境中此类矩阵的最大后验估计产生治疗，包括贝叶斯证据和可归因于Rougier and Priebe（2019）的灵活性罚款。我们还展示了如何使用两个数据驱动的示例在随机截距模型中如何使用先验来自然测试类内相关性的阳性。
We discuss Bayesian inference for a known-mean Gaussian model with a compound symmetric variance-covariance matrix. Since the space of such matrices is a linear subspace of that of positive definite matrices, we utilize the methods of Pisano (2022) to decompose the usual Wishart conjugate prior and derive a closed-form, three-parameter, bivariate conjugate prior distribution for the compound-symmetric half-precision matrix. The off-diagonal entry is found to have a non-central Kummer-Beta distribution conditioned on the diagonal, which is shown to have a gamma distribution generalized with Gauss's hypergeometric function. Such considerations yield a treatment of maximum a posteriori estimation for such matrices in Gaussian settings, including the Bayesian evidence and flexibility penalty attributable to Rougier and Priebe (2019). We also demonstrate how the prior may be utilized to naturally test for the positivity of a common within-class correlation in a random-intercept model using two data-driven examples.
