Model Uncertainty in Prediction, Variable Selection and Related Decision Problems

预测、变量选择和相关决策问题中的模型不确定性

• 批准号: 9626135
• 负责人: Merlise Clyde
• 金额: $ 7.9万
• 依托单位: Duke University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-07-01 至 2000-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9626135&HistoricalAwards=false
• 关键词: Model; Uncertainty; Prediction; Variable; Selection

DMS 9626135 Clyde Statistical predictions based on complex models may be very sensitive to modeling assumptions, such as choice of covariates. As a result, choosing a single model may not lead to satisfactory predictions and may significantly underestimate prediction intervals due to not incorporating uncertainty about the model choice into the final answer. Model uncertainty often outweighs other sources of uncertainty in problems, but is often ignored. Bayesian methods offer a very effective and conceptually appealing alternative: predictions and inferences can be based on a set of models rather than a single model; each model contributes proportionally to the support it receives from the observed data. This research involves Bayesian methods for stochastically searching high dimensional model spaces. As the number of models is very large, the challenge is therefore that of finding efficient ways of exploring the space of models, selecting plausible ones, and attributing to each of them a weight (approximating the posterior probability) for the mixing-based prediction or other utility calculations. Examples for the methodology include applications in wavelets and generalized additive models: calibration and prediction in spectroscopy using wavelet packets; determining the influence of particulate matter on mortality adjusting for other covariates in the presence of model uncertainty; and variable selection and prediction in binary regression models for seedling survival. Model averaging using importance sampling to sample from high dimensional model spaces is an effective solution. This approach is extended to selecting transformations of variables, subspace selection and thresholding in wavelets, and generalized additive models in the applications described above. Methods for sampling models with a probability proportional to their expected utility are also developed. %%% Finding and using models to describe data is a fundamental problem in both statis tics and the sciences. Statistical predictions may be very sensitive to the set of explanatory variables included in a model. Selecting a particular model based on selecting a subset of the explanatory variables and using this model for prediction, may lead to riskier decisions due to not incorporating uncertainty about model choice into the final answer. Model uncertainty often outweighs other sources of uncertainty in problems, but is usually ignored. In this research, predictions and inferences can be based on a set of models rather than a single model; each model contributes to the decision proportionally to the support it receives from the observed data. As the number of possible models is very large, the challenge is therefore that of finding efficient ways of exploring the space of models, selecting plausible ones, and attributing to each of them a weight for the weighted prediction or other decisions. The methodological developments are driven by the following applications: calibration and prediction in spectroscopy; and determining the influence of particulate matter on mortality adjusting for other meteorological variables when there is uncertainty about which variables should be included in the prediction model. ***

DMS 9626135基于复杂模型的CLYDE统计预测可能对建模假设（例如协变量的选择）非常敏感。 结果，选择单个模型可能不会导致令人满意的预测，并且由于未将模型选择的不确定性纳入最终答案，因此可能会大大低估预测间隔。 模型不确定性通常大于问题中其他不确定性的来源，但经常被忽略。贝叶斯方法提供了一种非常有效和概念上有吸引力的替代方法：预测和推论可以基于一组模型，而不是单个模型； 每个模型都会与观察到的数据获得的支持成比例地贡献。这项研究涉及用于随机搜索高维模型空间的贝叶斯方法。 因此，由于模型的数量非常大，因此挑战是寻找有效的方法来探索模型空间，选择合理的方法，并归因于每个模型的重量（近似于后验概率），以进行基于混合的预测或其他实用程序计算。 该方法的示例包括在小波和广义添加模型中的应用：使用小波数据包进行光谱中的校准和预测；在存在模型不确定性的情况下，确定颗粒物问题对其他协变量调整死亡率的影响；以及用于幼苗生存的二元回归模型中的可变选择和预测。 使用重要性抽样对从高维模型空间进行采样的模型平均是一个有效的解决方案。 这种方法扩展到选择变量的转换，小波中的子空间选择和阈值，以及上述应用中的广义加法模型。 还开发了与其预期效用成正比的采样模型的方法。 在Statis Tics和Sciences中，查找和使用模型描述数据是一个基本问题。 统计预测可能对模型中包含的一组解释变量非常敏感。 选择一个基于选择解释变量子集的特定模型并使用此模型进行预测，可能会导致风险更大的决策，因为没有将模型选择的不确定性纳入最终答案。 模型不确定性通常超过了问题中其他不确定性的来源，但通常被忽略。 在这项研究中，预测和推论可以基于一组模型，而不是单个模型。每个模型都与观察到的数据获得的支持成比例地促进了决策。因此，由于可能的模型数量很大，因此挑战是寻找有效的方法来探索模型空间，选择合理的模型，并归因于每个模型的权重以进行加权预测或其他决策。方法论发展是由以下应用驱动的：光谱法的校准和预测；并确定颗粒物对其他气象变量调整死亡率的影响，当存在不确定性中应包括哪些变量。 ***