Catching Up Faster in Bayesian Model Selection and Model Averaging
Catching Up Faster in Bayesian Model Selection and Model Averaging
复制标题
在贝叶斯模型选择和模型平均方面更快地赶上
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
S. D. Rooij
中科院分区：
文献类型：
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作者：
T. Erven;P. Grünwald;S. D. Rooij
贝叶斯模型平均、模型选择及其近似（如BIC）通常在统计上是一致的，但有时收敛速度比其他方法（如AIC和留一交叉验证）慢。另一方面，这些其他方法可能不一致。我们确定的追赶现象作为一个新的解释贝叶斯方法收敛速度慢。基于这种分析，我们定义了开关分布，贝叶斯模型平均分布的修改。我们证明了在许多情况下，基于开关分布的模型选择和预测是一致的，并达到最佳的收敛速度，从而解决了AIC-BIC困境。该方法是实用的，我们给出了一个有效的算法。
Bayesian model averaging, model selection and their approximations such as BIC are generally statistically consistent, but sometimes achieve slower rates of convergence than other methods such as AIC and leave-one-out cross-validation. On the other hand, these other methods can be inconsistent. We identify the catch-up phenomenon as a novel explanation for the slow convergence of Bayesian methods. Based on this analysis we define the switch-distribution, a modification of the Bayesian model averaging distribution. We prove that in many situations model selection and prediction based on the switch-distribution is both consistent and achieves optimal convergence rates, thereby resolving the AIC-BIC dilemma. The method is practical; we give an efficient algorithm.