论文标题
在层次贝叶斯推论中的蒙特卡洛总和的精确要求
Precision Requirements for Monte Carlo Sums within Hierarchical Bayesian Inference
论文作者
论文摘要
经常进行层次贝叶斯的推断，以估计来自蒙特卡洛总和对层次结构的单独分析或用于估计目标群体敏感性的模拟观察结果的样品的估计。我们调查对保证目标分布估计器所需的蒙特卡洛样品数量的需求，足够精确，以至于不会影响推理。我们考虑了如何生成蒙特卡洛样品的概率模型，这表明有限的样品数量引入了额外的不确定性，因为它们充当了层次可能性的组件的不完善编码。此外，我们研究了在不确定性的近似度量中被边缘化的估计量的行为，将其性能与蒙特卡洛点估计值进行了比较。我们发现，参数空间附近点的估计器之间的相关性对于估计值的精度至关重要。忽略这些相关性的近似边缘化将在推理中引入偏见，要么比具有点估计值构建的推论更昂贵（需要更多的蒙特卡洛样品）。因此，我们建议具有凭经验估计的目标分布使用点估计值的分层推论。
Hierarchical Bayesian inference is often conducted with estimates of the target distribution derived from Monte Carlo sums over samples from separate analyses of parts of the hierarchy or from mock observations used to estimate sensitivity to a target population. We investigate requirements on the number of Monte Carlo samples needed to guarantee the estimator of the target distribution is precise enough that it does not affect the inference. We consider probabilistic models of how Monte Carlo samples are generated, showing that the finite number of samples introduces additional uncertainty as they act as an imperfect encoding of the components of the hierarchical likelihood. Additionally, we investigate the behavior of estimators marginalized over approximate measures of the uncertainty, comparing their performance to the Monte Carlo point estimate. We find that correlations between the estimators at nearby points in parameter space are crucial to the precision of the estimate. Approximate marginalization that neglects these correlations will either introduce a bias within the inference or be more expensive (require more Monte Carlo samples) than an inference constructed with point estimates. We therefore recommend that hierarchical inferences with empirically estimated target distributions use point estimates.
