We propose a new fiducial Markov Chain Monte Carlo (MCMC) method for fitting parametric Gaussian models. We utilize the Cayley transform to decompose the parametric covariance matrix, which in turn allows us to formulate a general data generating algorithm for Gaussian data. Leveraging constrained generalized fiducial inference, we are able to create the basis of an MCMC algorithm, which can be specified to parametric models with minimal effort. The appeal of this novel approach is the wide class of models which it permits, ease of implementation and the posterior-like fiducial distribution without the need for a prior. We provide background information for the derivation of the relevant fiducial quantities, and a proof that the proposed MCMC algorithm targets the correct fiducial distribution. We need not assume independence nor identical distribution of the data, which makes the method attractive for application to time series and spatial data. Well-performing simulation results of the MA(1) and Matérn models are presented.

翻译：我们提出了一种新的基准马尔可夫链蒙特卡洛（MCMC）方法，用于拟合参数化高斯模型。我们利用凯莱变换对参数协方差矩阵进行分解，从而能够构建高斯数据的通用数据生成算法。借助约束广义基准推断，我们得以构建MCMC算法的基础框架，该框架可轻松适配于各类参数模型。这一新方法的吸引力在于其适用于广泛的模型类别、易于实现，并且能产生类似后验的基准分布而无需先验。我们提供了相关基准量推导的背景信息，并证明了所提出的MCMC算法能够收敛到正确的基准分布。该方法无需假设数据的独立同分布特性，使其在时间序列和空间数据分析中具有显著优势。文中展示了MA(1)模型与Matérn模型的高效仿真结果。