Analysing non-Gaussian spatial-temporal data typically requires introducing spatial dependence in generalised linear models through the link function of an exponential family distribution. However, unlike in Gaussian likelihoods, inference is considerably encumbered by the inability to analytically integrate out the random effects and reduce the dimension of the parameter space. Iterative estimation algorithms struggle to converge due to the presence of weakly identified parameters. We devise an approach that obviates these issues by exploiting generalised conjugate multivariate distribution theory for exponential families, which enables exact sampling from analytically available posterior distributions conditional upon some fixed process parameters. More specifically, we expand upon the Diaconis-Ylvisaker family of conjugate priors to achieve analytically tractable posterior inference for spatially-temporally varying regression models conditional on some kernel parameters. Subsequently, we assimilate inference from these individual posterior distributions over a range of values of these parameters using Bayesian predictive stacking. We evaluate inferential performance on simulated data, compare with fully Bayesian inference using Markov chain Monte Carlo and apply our proposed method to analyse spatially-temporally referenced avian count data from the North American Breeding Bird Survey database.

翻译：分析非高斯时空数据通常需要在广义线性模型中通过指数族分布的链接函数引入空间依赖性。然而，与高斯似然不同，由于无法解析地积分掉随机效应并降低参数空间的维度，推断过程受到显著阻碍。存在弱识别参数时，迭代估计算法难以收敛。我们设计了一种方法，通过利用指数族的广义共轭多元分布理论来避免这些问题，该理论能够在给定某些固定过程参数的条件下，从解析可得的后验分布中进行精确采样。具体而言，我们扩展了Diaconis-Ylvisaker共轭先验族，以实现对依赖于某些核参数的时空变化回归模型进行解析易处理的后验推断。随后，我们使用贝叶斯预测堆叠方法，将这些参数在一系列取值下的各个后验分布推断结果进行融合。我们在模拟数据上评估了推断性能，与使用马尔可夫链蒙特卡洛的完全贝叶斯推断进行了比较，并将我们提出的方法应用于分析来自北美繁殖鸟类调查数据库的时空参考鸟类计数数据。