We consider a class of latent Gaussian models with a univariate link function (ULLGMs). These are based on standard likelihood specifications (such as Poisson, Binomial, Bernoulli, Erlang, etc.) but incorporate a latent normal linear regression framework on a transformation of a key scalar parameter. We allow for model uncertainty regarding the covariates included in the regression. The ULLGM class typically accommodates extra dispersion in the data and has clear advantages for deriving theoretical properties and designing computational procedures. We formally characterize posterior existence under a convenient and popular improper prior and propose an efficient Markov chain Monte Carlo algorithm for Bayesian model averaging in ULLGMs. Simulation results suggest that the framework provides accurate results that are robust to some degree of misspecification. The methodology is successfully applied to measles vaccination coverage data from Ethiopia and to data on bilateral migration flows between OECD countries.

翻译：我们考虑一类具有单变量链接函数的潜高斯模型。这类模型基于标准似然设定（如泊松分布、二项分布、伯努利分布、埃尔朗分布等），但在关键标量参数的变换上引入了潜正态线性回归框架。我们允许回归中包含的协变量存在模型不确定性。ULLGM类模型通常能够适应数据中的额外离散性，并且在推导理论性质和设计计算流程方面具有明显优势。我们在一种便捷且常用的非信息先验下，正式刻画了后验分布的存在性，并提出了一种高效的马尔可夫链蒙特卡洛算法，用于ULLGM中的贝叶斯模型平均。模拟结果表明，该框架能够提供准确的结果，并且在一定程度上对设定误设具有稳健性。该方法已成功应用于埃塞俄比亚的麻疹疫苗接种覆盖率数据以及经合组织国家间的双边移民流动数据。