ASSESSMENT AND PROPAGATION OF MODEL UNCERTAINTY

• 成果类型: Article
• 署名作者: DRAPER, D
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/j.2517-6161.1995.tb02015.x
• 发表日期: 1995
• 页码: 45-97
• 关键词: maximum-likelihood; time-series; regression; inference; selection; experiences; ORDER; AGE

摘要

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.