A wide class of Bayesian models involve unidentifiable random matrices that display rotational ambiguity, with the Gaussian factor model being a typical example. A rich variety of Markov chain Monte Carlo (MCMC) algorithms have been proposed for sampling the parameters of these models. However, without identifiability constraints, reliable posterior summaries of the parameters cannot be obtained directly from the MCMC output. As an alternative, we propose a computationally efficient post-processing algorithm that allows inference on non-identifiable parameters. We first orthogonalize the posterior samples using Varimax and then tackle label and sign switching with a greedy matching algorithm. We compare the performance and computational complexity with other methods using a simulation study and chemical exposures data. The algorithm implementation is available in the infinitefactor R package on CRAN.

翻译：一类广泛的贝叶斯模型涉及具有旋转模糊性的不可识别随机矩阵，其中高斯因子模型是典型示例。已有多种马尔可夫链蒙特卡洛（MCMC）算法被提出用于对这些模型的参数进行抽样。然而，在缺乏可识别性约束的情况下，无法直接从MCMC输出中获得可靠的参数后验摘要。作为替代方案，我们提出了一种计算高效的后处理算法，该算法支持对不可识别参数进行推断。我们首先使用最大方差旋转法对后验样本进行正交化处理，随后通过贪心匹配算法解决标签切换和符号切换问题。我们通过模拟研究和化学暴露数据，将该方法的性能及计算复杂度与其他方法进行了比较。算法实现已发布于CRAN平台的infinitefactor R程序包中。