Bayes model averaging with selection of regressors
Bayes model averaging with selection of regressors
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DOI：
10.1111/1467-9868.00348
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发表时间：
2002-01-01
影响因子：
5.8
通讯作者：
Fearn, T
中科院分区：
文献类型：
--
作者：
Brown, PJ;Vannucci, M;Fearn, T
当多个不同的模型竞争用于预测时，选择单个模型可能会提供相当不稳定的预测结果。在回归分析中，贝叶斯模型平均的随机搜索变量选择为解决这个稳健性问题提供了一种方法，但代价是需要大量的预测变量。在这里，我们研究结合变量选择用于预测的贝叶斯模型平均。这提供了相似的预测均方误差，但预测变量空间大幅减少。这可以极大地有助于模型的解释。如果测量变量有成本，它还能降低成本。这里的发展是在多元一般线性模型的背景下使用决策理论。顺便提一下，这种减少预测变量空间的贝叶斯模型平均与单模型近似进行了对比。开发了一种在马尔可夫链蒙特卡罗搜索中用于后验推断的快速更新回归算法，使得可以考虑比观测值多得多的变量。我们讨论了回归中绝对收缩而非比例收缩的优点，特别是当变量多于观测值时。该方法在一组用于测量水溶液中不同糖类含量的光谱数据上进行了说明。
When a number of distinct models contend for use in prediction, the choice of a single model can offer rather unstable predictions. In regression, stochastic search variable selection with Bayesian model averaging offers a cure for this robustness issue but at the expense of requiring very many predictors. Here we look at Bayes model averaging incorporating variable selection for prediction. This offers similar mean-square errors of prediction but with a vastly reduced predictor space. This can greatly aid the interpretation of the model. It also reduces the cost if measured variables have costs. The development here uses decision theory in the context of the multivariate general linear model. In passing, this reduced predictor space Bayes model averaging is contrasted with single-model approximations. A fast algorithm for updating regressions in the Markov chain Monte Carlo searches for posterior inference is developed, allowing many more variables than observations to be contemplated. We discuss the merits of absolute rather than proportionate shrinkage in regression, especially when there are more variables than observations. The methodology is illustrated on a set of spectroscopic data used for measuring the amounts of different sugars in an aqueous solution.