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A Bayes Linear Bayes Method for Estimation of Correlated Event Rates

机译：估计相关事件发生率的贝叶斯线性贝叶斯方法

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摘要

Typically, full Bayesian estimation of correlated event rates can be computationally challenging since estimators are intractable. When estimation of event rates represents one activity within a larger modeling process, there is an incentive to develop more efficient inference than provided by a full Bayesian model. We develop a new subjective inference method for correlated event rates based on a Bayes linear Bayes model under the assumption that events are generated from a homogeneous Poisson process. To reduce the elicitation burden we introduce homogenization factors to the model and, as an alternative to a subjective prior, an empirical method using the method of moments is developed. Inference under the new method is compared against estimates obtained under a full Bayesian model, which takes a multivariate gamma prior, where the predictive and posterior distributions are derived in terms of well-known functions. The mathematical properties of both models are presented. A simulation study shows that the Bayes linear Bayes inference method and the full Bayesian model provide equally reliable estimates. An illustrative example, motivated by a problem of estimating correlated event rates across different users in a simple supply chain, shows how ignoring the correlation leads to biased estimation of event rates.
机译：通常，由于估计器难以处理，因此相关事件发生率的完整贝叶斯估计可能在计算上具有挑战性。当事件发生率的估计代表较大建模过程中的一项活动时，就有动机去开发比完整贝叶斯模型所提供的更有效的推理。我们假设事件是从均匀的Poisson过程生成的，因此基于Bayes线性Bayes模型，开发了一种用于相关事件发生率的主观推断新方法。为了减少启发负担，我们向模型中引入了均化因子，并且作为主观先验的替代方法，开发了一种采用矩量法的经验方法。将新方法下的推论与在完整贝叶斯模型下获得的估计值进行比较，该模型采用多元伽马先验，其中预测和后验分布是根据众所周知的函数得出的。给出了两个模型的数学性质。仿真研究表明，贝叶斯线性贝叶斯推断方法和完整的贝叶斯模型可提供同样可靠的估计。由在简单的供应链中估计不同用户之间的相关事件发生率的问题所激发的说明性示例示出了如何忽略相关性导致事件发生率的估计有偏差。

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