Many statistical problems in causal inference involve a probability distribution other than the one from which data are actually observed; as an additional complication, the object of interest is often a marginal quantity of this other probability distribution. This creates many practical complications for statistical inference, even where the problem is non-parametrically identified. In particular, it is difficult to perform likelihood-based inference, or even to simulate from the model in a general way. We introduce the `frugal parameterization', which places the causal effect of interest at its centre, and then builds the rest of the model around it. We do this in a way that provides a recipe for constructing a regular, non-redundant parameterization using causal quantities of interest. In the case of discrete variables we can use odds ratios to complete the parameterization, while in the continuous case copulas are the natural choice; other possibilities are also discussed. Our methods allow us to construct and simulate from models with parametrically specified causal distributions, and fit them using likelihood-based methods, including fully Bayesian approaches. Our proposal includes parameterizations for the average causal effect and effect of treatment on the treated, as well as other causal quantities of interest.
翻译:在因果推断中,许多统计问题涉及的概率分布,不是数据实际观察到的概率分布;作为额外的复杂因素,利息对象往往是其他概率分布的边际数量。这给统计推论造成许多实际的复杂因素,即使问题不是参数性的。特别是,很难进行基于可能性的推论,甚至很难从模型中一般性地模拟。我们采用“节制参数化”,将利息的因果关系置于其中心,然后建立模型的其余部分。我们这样做的方式是利用因果数量来建立定期的、非冗余的参数化。就离散变量而言,我们可以使用概率比来完成参数化,而就连续的情况而言,可进行自然选择;还讨论其他可能性。我们的方法使我们能够从模型中构建和模拟具有参数性说明因果分布的模型,并使用基于概率的方法,包括完全的Bayesian方法。我们的提议包括平均因果影响参数化和处理因果量的参数,作为利息处理的参数。