ASSESSMENT AND PROPAGATION OF MODEL UNCERTAINTY
ASSESSMENT AND PROPAGATION OF MODEL UNCERTAINTY
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DOI：
10.1111/j.2517-6161.1995.tb02015.x
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发表时间：
1995-01-01
影响因子：
5.8
通讯作者：
DRAPER, D
中科院分区：
文献类型：
--
作者：
DRAPER, D
在大多数推理和预测的例子中，基于已知量x的关于未知量y的不确定性的表达是基于模型M的，该模型M形式化了关于x和y如何相关的假设。M通常有两个部分：结构假设S，例如广义线性模型中的链接函数的形式和误差分布的选择，以及参数θ，其含义特定于S的给定选择。在统计理论和实践中，通常承认给定特定假设结构S的θ的参数不确定性;承认S本身的结构不确定性则不太常见。一种广泛使用的方法是借助x来为S指定一个似乎合理的单一“最佳”选择S*，然后继续进行，就好像S* 是正确的一样。一般来说，这种方法不能充分评估和传播结构不确定性，并可能导致在给定x的情况下对y的不确定性评估出现错误。当发生错误校准时，它通常会导致对y的推断或预测不确定性的低估，导致不准确的科学总结和过度自信的决策，这些决策没有充分地对冲不确定性。在本文中，我讨论了贝叶斯方法来解决这个问题，长期以来一直在原则上，但现在才成为常规可行的，凭借最近的计算进步，并检查其实施的例子，涉及预测石油价格和估计的机会灾难性失败的美国航天飞机。
In most examples of inference and prediction, the expression of uncertainty about unknown quantities y on the basis of known quantities x is based on a model M that formalizes assumptions about how x and y are related. M will typically have two parts: structural assumptions S, such as the form of the link function and the choice of error distribution in a generalized linear model, and parameters theta whose meaning is specific to a given choice of S. It is common in statistical theory and practice to acknowledge parametric uncertainty about theta given a particular assumed structure S; it is less common to acknowledge structural uncertainty about S itself. A widely used approach involves enlisting the aid of x to specify a plausible single 'best' choice S* for S, and then proceeding as if S* were known to be correct. In general this approach fails to assess and propagate structural uncertainty fully and may lead to miscalibrated uncertainty assessment about y given x. When miscalibration occurs it will often result in understatement of inferential or predictive uncertainty about y, leading to inaccurate scientific summaries and overconfident decisions that do not incorporate sufficient hedging against uncertainty. In this paper I discuss a Bayesian approach to solving this problem that has long been available in principle but is only now becoming routinely feasible, by virtue of recent computational advances, and examine its implementation in examples that involve forecasting the price of oil and estimating the chance of catastrophic failure of the US space shuttle.