Although Bayesian skew-normal models are useful for flexibly modeling spatio-temporal processes, they still have difficulty in computation cost and interpretability in their mean and variance parameters, including regression coefficients. To address these problems, this study proposes a spatio-temporal model that incorporates skewness while maintaining mean and variance, by applying the flexible subclass of the closed skew-normal distribution. An efficient sampling method is introduced, leveraging the autoregressive representation of the model. Additionally, the model's symmetry concerning spatial order is demonstrated, and Mardia's skewness and kurtosis are derived, showing independence from the mean and variance. Simulation studies compare the estimation performance of the proposed model with that of the Gaussian model. The result confirms its superiority in high skewness and low observation noise scenarios. The identification of Cobb-Douglas production functions across US states is examined as an application to real data, revealing that the proposed model excels in both goodness-of-fit and predictive performance.

翻译：尽管贝叶斯斜正态模型能够灵活建模时空过程，但其在计算成本以及均值、方差参数（包括回归系数）的可解释性方面仍存在困难。为解决这些问题，本研究通过应用闭斜正态分布的灵活子类，提出了一种在保持均值与方差的同时纳入偏斜特性的时空模型。该模型利用其自回归表示形式，引入了一种高效的抽样方法。此外，研究证明了模型关于空间顺序的对称性，并推导了Mardia偏度与峰度，表明二者独立于均值与方差。模拟研究比较了所提模型与高斯模型的估计性能，结果证实了该模型在高偏斜度与低观测噪声场景下的优越性。通过对美国各州Cobb-Douglas生产函数的识别进行实证数据分析，表明所提模型在拟合优度与预测性能方面均表现优异。