Bayesian inference for generalized linear models via quasi-posteriors
针对广义线性模型因模型设定错误导致推断不稳健的问题，提出基于拟后验分布的贝叶斯推断方法，该方法在稳健性和频率覆盖上表现良好，并给出损失尺度参数的矩估计。
Generalized linear models are routinely used for modelling relationships between a response variable and a set of covariates. The simple form of a generalized linear model comes with easy interpretability, but also leads to concerns about model misspecification impacting inferential conclusions. A popular semiparametric solution adopted in the frequentist literature is quasilikelihood, which improves robustness by only requiring correct specification of the first two moments. We develop a robust approach to Bayesian inference in generalized linear models through quasi-posterior distributions. We show that quasi-posteriors provide a coherent generalized Bayes inference method, while also approximating so-called coarsened posteriors. In so doing, we obtain new insights into the choice of coarsening parameter. Asymptotically, the quasi-posterior converges in total variation to a normal distribution and has important connections with the loss-likelihood bootstrap posterior. We demonstrate that it is also well calibrated in terms of frequentist coverage. Moreover, the loss-scale parameter has a clear interpretation as a dispersion, and this leads to a consolidated method-of-moments estimator.