A statistical method for the elicitation of priors in Bayesian generalised linear models (GLMs) and extensions is proposed. Probabilistic predictions are elicited from the expert to parametrise a multivariate t prior distribution for the unknown linear coefficients of the GLM and an inverse gamma prior for the dispersion parameter, if unknown. The elicited predictions condition on defined elicitation scenarios. Dependencies among scenarios are then elicited from the expert by additionally conditioning on hypothetical experiments. Elicited conditional medians efficiently parametrise a canonical vine copula model of dependence that may be truncated for efficiency. The statistical elicitation method permits prior parametrisation of GLMs with alternative choices of design matrices or observation models from the same elicitation session. Extensions of the method apply to multivariate data, data with bounded support, semi-continuous data with point mass at zero, and count data with overdispersion or zero-inflation. A case study elicits a prior for an extended GLM embedded in a statistical model of overdispersed counts described by a binomial-simplex mixture distribution. The elicited canonical vine model of dependence is found to incorporate substantial information into the prior. The procedures of the statistical elicitation method are implemented in the R package eglm.

翻译：提出了一种用于贝叶斯广义线性模型（GLM）及其扩展中先验分布的统计启发方法。通过从专家处获取概率预测，对GLM中未知线性系数参数化多元t先验分布，并对未知的离散参数参数化逆伽马先验分布。所获取的预测基于定义的启发场景条件化。随后，通过额外假设实验条件化，从专家处获取场景间的依赖关系。获取的条件中位数有效参数化可因效率而截断的标准藤蔓copula依赖模型。该统计启发方法允许在同一次启发会话中，基于不同设计矩阵或观测模型选择对GLM进行先验参数化。该方法的扩展适用于多元数据、有界支撑数据、含零点质量点半连续数据，以及过度离散或零膨胀计数数据。案例研究展示了如何为嵌入二项式-单纯形混合分布描述的过度离散计数统计模型中的扩展GLM获取先验。研究发现，所获取的标准藤蔓依赖模型为先验融入了大量信息。该统计启发方法的流程已在R软件包eglm中实现。